MANONMANIAM SUNDARANAR UNIVERSITY, TIRUNELVELI(For those candidates who joined 2014-2015 and onwards)

M.Sc., STATISTICS (Choice Based Credit System)

1. Eligibility criteria for admission:A candidate who has passed (i) B.Sc. Degree with Statistics / Mathematics as the main

subject or (ii) B.Sc., Degree with Computer Science / Information Technology / Physics as the main subject and Mathematics as an allied or ancillary subject with 45% Marks (40% in the case of SC/ST) in aggregate in Part III shall be permitted to join the course and to appear in this University examination and to qualify for the award of M.Sc., (STATISTICS) degree after a course of study of two academic years in the University Department of Statistics.

2. Scheme of Examination:---------------------------------------------------------------------------------------

Semester/ Title Level Credits Exam Max Passing Teachingof the papers Core /Elective/supportive Hours Marks Marks Hours

----------------------------------------------------------------------------------------I SEMESTER 1.1 REAL ANALYSIS AND

LINEAR ALGEBRA core 4 3 Hrs 100 50% 3L+1T1.2 PROBABILITY THEORY core 4 3 Hrs 100 50% 3L+1T+1P1.3 DISTRIBUTION THEORY core 4 3 Hrs 100 50% 3L+1T+1P1.4 SAMPLE SURVEYS core 4 3 Hrs 100 50% 3L+1T+1P1.5 ELECTIVE - I elective 5 3 Hrs 100 50% 2L+1T+2P

II SEMESTER 2.1 STATISTICAL INFERENCE –I core 4 3 Hrs 100 50% 3L+1T+1P2.2 STOCHASTIC PROCESSES core 4 3 Hrs 100 50% 3L+1T2.3 STATISTICAL QUALITY CONTROL core 4 3 Hrs 100 50% 3L+1T+1P AND RELIABILITY2.4 OPERATIONS RESEARCH core 4 3 Hrs 100 50% 2L+1T+2P2.5 SUPPORTIVE PAPER-I* supportive 4 3 Hrs 100 50% ---2.6 STATISTICS PRACTICAL core 4 3 Hrs 100 50% 2L+1T+2P

USING SOFTWARE - I

III SEMESTER3.1 STATISTICAL INFERENCE - II core 4 3 Hrs 100 50% 3L+1T+1P3.2 MULTIVARIATE ANALYSIS core 4 3 Hrs. 100 50% 3L+1T+1P3.3 ECONOMETRICS core 4 3 Hrs. 100 50% 3L+1T3.4 DEMOGRAPHY core 4 3 Hrs. 100 50% 3L+1T+1P3.5 LINEAR MODELS AND DESIGN OF core 4 3 Hrs. 100 50% 3L+1T+1P

EXPERIMENTS3.6 SUPPORTIVE PAPER-II* supportive 4 3 Hrs. 100 50% ---

IV SEMESTER4.1 ELECTIVE - II elective 4 3 Hrs. 100 50% 3L+1T+1P4.2 ELECTIVE - III elective 4 3 Hrs. 100 50% 2L+1T+2P4.3 ELECTIVE - IV elective 4 3 Hrs. 100 50% 3L+1T+1P4.4 STATISTICS PRACTICAL core 4 3 Hrs. 100 50% 2L+1T+2P

USING SOFTWARE - II4.5 PROJECT AND VIVA-VOCE core 5 3 Hrs. 100 50% ---

---------------------------------------------------------------------------------------- TOTAL NUMBER OF CREDITS 90

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NOTE 1:

* Students of M.Sc., (Statistics) should select supportive courses offered by other Departments of the University.

NOTE 2: L: LECTURE T: TUTORIAL P: PRACTICAL

3. List of Elective Papers (Major):

ELECTIVE – I: (Any one of the following may be opted)

(i) PROGRAMMING IN C++ AND S-PLUS/R(ii) PROGRAMMING IN VISUAL BASIC (iii) COMPUTER SIMULATION AND MODELLING(iv) DATA MINING

ELECTIVE – II: (Any one of the following may be opted)

(i) APPLIED REGRESSION ANALYSIS(ii) RELIABILITY THEORY AND ITS APPLICATIONS(iii) ADVANCED STATISTICAL QUALITY CONTROL(iv) ACTUARIAL STATISTICS(v) FUZZY LOGIC AND ITS APPLICATIONS

ELECTIVE – III: (Any one of the following may be opted)

(i) DATA ANALYSIS USING SOFTWARE(ii) DIRECTIONAL DATA ANALYSIS (iii) CATEGORICAL DATA ANALYSIS (iv) OFFICIAL STATISTICS(v) STATISTICAL METHODS FOR BIOINFORMATICS (vi) FINANCIAL STATISTICS

ELECTIVE – IV: (Any one of the following may be opted)

(i) TIME SERIES ANALYSIS(ii) STATISTICAL METHODS IN EPIDEMIOLOGY(iii) BAYESIAN METHODS(iv) DATA STRUCTURES (v) STATISTICAL DECISION THEORY(vi) GAME THEORY AND ITS APPLICATIONS

4. List of Supportive Papers (Non-Major):The following supportive courses will be offered by the Department of Statistics to the

post- graduate students studying in other Academic Departments in the University.

(i) DESCRIPTIVE STATISTICS(ii) STATISTICS FOR BEHAVIOURAL SCIENCES(iii) COMPUTER ORIENTED STATISTICAL METHODS(iv) PROBABILITY AND STATISTICS(v) STATISTICAL METHODS (vi) BIO-STATISTICS(vii) MATHEMATICAL ECONOMICS(viii) ADVANCED STATISTICAL METHODS

5. Objective of the Course:This course aims to train the students in the selection and applications of Statistical methods

for analyzing data arising in the real world problems. It also aims to provide practical experience in carrying out data analysis using statistical software SAS, S-PLUS and SPSS.

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6. Examination:

Each candidate admitted to the course will be examined in each paper under Continuous Internal Assessment by the course teacher and by end semester University Examination. The weightage of marks of continuous Internal Assessment system and end semester University Examination shall be 25:75.

Each admitted candidate shall have to carry out a project work during the fourth semester under the supervision of the faculty members of the University Department of Statistics. Each candidate shall have to prepare and submit a report of the project work at the end of the fourth semester. The project report will be evaluated for a maximum of 80 marks. Each candidate shall appear for a Viva-Voce examination for a maximum of 20 marks.

QUESTION PAPER PATTERN FOR UNIVERSITY EXAMINATIONM.Sc., Degree Examination

Branch II – Statistics Time: 3 Hours Max. Marks: 75

Section - A (5 × 2 =10)Answer any FIVE questions

Each question carries 2 marks1.2.3.4.5.6.7.8.

Section - B (5 × 5 = 25 Marks)5 Questions (One question from each Unit) with internal choice

Each question carries 5 marks 9. (a)

(OR) (b)

10. (a)

(OR) (b)

11. (a)

(OR) (b)

12. (a)

(OR) (b)

13. (a)

(OR) (b)

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Section – C (5 × 8 = 40 marks)5 Questions (One question from each Unit) with internal choice.

Each question carries 8 marks14. (a)

(OR) (b)

15. (a)

(OR) (b)

16. (a)

(OR) (b)

17. (a)

(OR) (b)

18. (a)

(OR) (b)

7. Award of Degree

A candidate who has secured minimum of 50% marks in end semester University Examination as well as 50% marks comprising both continuous Internal Assessment and end semester University Examination in each paper shall be declared to have passed the M.Sc., degree course in Statistics.

A candidate who has secured minimum of 60% marks comprising both continuous Internal Assessment and end semester University Examination in aggregate shall be declared to have passed M.Sc., degree course in Statistics with FIRST class.

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SYLLABUS FOR CORE PAPERS

I SEMESTER1.1 REAL ANALYSIS AND LINEAR ALGEBRA

UNIT IIntroduction to n-dimensional Euclidean space and metric space – Countability, supremum

and infimum of sets of real numbers – Bolzano-Weirstrass theorem. Convergence of sequences and series of real numbers – absolute and conditional convergence – Point-wise and uniform convergence – Tests for absolute, conditional and uniform convergence – Properties of uniform convergence.

UNIT IIReal valued functions - Limits and continuity and uniform continuity – Differentiability –

Maxima and Minima of functions – mean value theorem, Taylor’s theorem – functions of several variables.

UNIT IIIRiemann-Stieltjes sums – Riemann-Stieltjes integral – Properties and Evaluation –

Fundamental theorem – Differentiation under integral sign – Leibnitz’s rule - Improper integrals - Multiple integrals and their evaluation by repeated integration.

UNIT IVVector spaces and subspaces – linear dependence – dimension and basis of a vector space –

linear transformation - Orthogonality – Orthonormal basis – Gram-Schmidt orthogonalization process – Inner product space.

UNIT VMatrices – Rank and inverse of matrices – properties – Eigen values and Eigenvectors –

Idempotent and partitioned matrices – Generalized inverse and its determination - Reduction of matrices into diagonal, echelon, canonical and triangular forms - Quadratic forms – Reduction and classification of quadratic forms – Cochran’s theorem.

BOOKS FOR STUDY:1. Arora, S. (1988): Real Analysis. Satya Prakashan Mandir, New Delhi.2. Apostol, T.M. (1974): Mathematical Analysis (Second Edition). Addison-Wesley,

New York. (Twentieth Reprint, 2002).3. Goldberg, R. (1976). Methods of Real Analysis (Second Edition).Oxford & IBH Publishing

Co., New Delhi.4. Hadley, G. (1987). Linear Algebra. Narosa Publishing House, New Delhi.5. Malik, S.C. and Arora, S. (2009). Mathematical Analysis (Second Edition). New Age

Science Limited.6. Miller, K.S. (1957): Advanced Real Calculus. Krieger Publishing Company.7. Ramachandra Rao, A. and Bhimasankaram, P. (2000): Linear Algebra. Hindustan Book

Agency, Hyderabad.8. Rao, C.R. (1973). Linear Statistical Inference and Its Applications (Second Edition). Wiley

Eastern Limited, New Delhi.9. Rudin, W. (1985): Principles of Mathematical Analysis (Third Edition). McGraw Hill,

New York.10. Searle, S.R. (1982). Matrix Algebra Useful for Statistics. Wiley-Interscience, New York.

(Reprint,2006)11. Vasistha, A.R. (2005): Matrices. Krishna Prakashan Mandir, New Delhi.

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1.2 PROBABILITY THEORYUNIT I

Classes of sets - ring - field - σ-field - minimal σ-field - Borel field - sequences of sets - limit inferior and limit superior of sequences of sets - Measurable space - measure space – properties of measure - Lebesgue measure and Lebesgue-Stieltjes measure - Probability space - probability measure – properties of probability measure.

UNIT IIMeasurable function – random variable – distribution function – discrete and continuous

random variables – decomposition of distribution functions - Expectation and moments – properties – generating functions - Chebyshev’s, Markov’s, Holder’s, Jensen’s and Minkowski’s inequalities - Characteristic function – inversion theorem and its applications – Uniqueness theorem – Khintchine- Bochner’s theorem (statement only).

UNIT IIIModes of convergence – convergence in probability, convergence in distribution,

convergence in rth mean almost sure convergence and their interrelationships. Weak and complete convergences of distribution functions – Helly’s first and second limit theorems (statement only) and their applications.

UNIT IVIndependence of random variables – Borel-Cantelli lemma – Kolmogorov’s 0-1 law.

Kolmogorov’s inequality – Khintchine’s weak law of large numbers and Kolmogorov’s weak law of large numbers – Kolmogorov’s strong law of large numbers – Glivenko-Cantelli theorem (statement only).

UNIT VCentral limit theorems – De Moivre-Laplace central limit theorem, Lindeberg-Levy’s

central limit theorem, Liapunov’s central limit theorem – Lindeberg-Feller’s central limit theorem (statement only). Radon-Nikodym theorem and derivative (without proof) – conditional probability and conditional expectation – properties and applications. Product space – Fubini’s theorem (statement only) and its applications.

BOOKS FOR STUDY:1. Ash, B.R. (1972): Real Analysis and Probability. Academic Press, New York.2. Bhat, B.R.(1999): Modern Probability Theory (Third Edition). New Age International,

New Delhi.(Reprint 2004)3. Billingsley, P. (2012): Probability and Measure (Third Edition). John Wiley & Sons, New York.4. Chow, Y.S. and Teicher, H. (2012): Probability Theory: Independence, Interchangeability,

Martingales (Second Edition). Springer Limited.5. Feller, W. (2008): An Introduction to Probability Theory and Its Applications, Volume I (Third Edition), John Wiley & Sons, New York. 6. Feller, W. (1971): An Introduction to Probability Theory and Its Applications, Volume II, John Wiley & Sons, New York. (Reprint, 2008).7. Loe’ve, M. (1978): Probability Theory (Fourth Edition). Springer-Verlag, New York.8. Rana, I.K. (2005): An Introduction to Measure and Integration (Second Edition). Morgan & Claypool.9. Rohatgi, V.K. and Saleh, A.K.Md.E. (2011): An Introduction to Probability and Statistics (Second Edition). John Wiley & Sons, New York. 10. Ross, S.M (2010). A First Course in Probability. Pearson Prentice Hall.

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1.3 DISTRIBUTION THEORYUNIT I

Basic distribution theory – Joint, marginal and conditional probability mass functions and probability density functions. Standard distributions: Binomial, Poisson, multinomial and Normal probability distributions. Bivariate normal distribution – Properties and relationships.

UNIT IIFunctions of random variables and their distributions – Methods of finding distributions:

Cumulative Distribution Function - Jacobian of transformation - Characteristic Function and Moment Generating Function - Mathematical Expectation and Conditional expectation.

UNIT III Geometric, Negative binomial, Truncated binomial, Truncated Poisson, Power series and

Logarithmic distributions – Properties and relationships.

UNIT IV Exponential, Laplace, logistic, log-normal, beta, gamma, Cauchy and compound Poisson

distribution. Sampling distributions - Central-t, Central-F, Central chi-square distributions – Properties and relationships.

UNIT V Non–central t - non–central chi-square - non-central F distributions and their properties.

Order statistics: Distribution of rth order statistics – Joint distribution of two or more order statistics - Distribution of sample range and median.

BOOKS FOR STUDY:1. Johnson, N.L., Kemp, A.W. and Kotz, S. (2005): Univariate Discrete Distributions (Third Edition). John Wiley & sons, New York. 2. Johnson, N.L, Kotz, S. and Balakrishnan, N. (2004): Continuous Univariate Distributions. Vol. I. John Wiley & sons (Asia), Singapore. 3. Johnson, N.L, Kotz, S. and Balakrishnan, N. (2014): Continuous Univariate Distributions. Vol. II. John Wiley & sons (Asia), Singapore.4. Karian, Z.A. and Dudewicz, E.J. (2011). Handbook of Fitting Statistical Distributions with

R. Chapman & Hall.5. Mood, A.M., Graybill, F.A. and Boes, D.C. (1974): Introduction to the Theory of Statistics (Third Edition). McGraw-Hill International Editions.6. Rao, C.R. (2009): Linear Statistical Inference and Its Applications (Second Edition). John Wiley & Sons.7. Rohatgi, V.K. and Saleh, A.K.Md.E. (2011): An Introduction to Probability and Statistics (Second Edition). John Wiley & Sons, New York.

1.4 SAMPLE SURVEYSUNIT I

Population and Sample – Census and sample survey – sampling – sampling unit, sampling frame, sampling distribution, standard error, questionnaire and schedule, sampling design – sampling and non-sampling errors – non response and its effects – sample surveys – principles of sample survey - principle steps in sample survey - limitations of sampling – NSSO/CSO in India.

UNIT II Simple Random Sampling (with and without replacement): Notations and terminology-

Estimates of population total, mean and their variances and standard errors - determination of sample size - pooling of estimates – confidence limits – simple random sampling of attributes – interpenetrating sub-samples.

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UNIT III Stratified random sampling estimates of population total, mean and their variances -

Related properties – Allocation of sample sizes – Neyman’s proportional and optimum allocations - Comparison of stratified sampling with simple random sampling - Estimation of proportion under stratified random sampling.

UNIT IV Systematic sampling: Estimates of population total, mean, and their variances and

standard errors – systematic sampling with linear trend – comparison of systematic sampling with stratified and simple random sampling – circular systematic sampling - Two stage sampling with equal number of second stage units and cluster sampling.

UNIT V Varying Probability Sampling: PPS sampling (with and without replacement) – gain due

to PPS sampling – stratified PPS – selection procedures – ordered and unordered estimates – Desraj, Horwitz – Thompson and Murthy’s estimates.

Ratio Estimate – Methods of estimation, approximate variance of the Ratio Estimate - Regression Estimators – Difference Estimators, Regression Estimators in Stratified Sampling - Double sampling.

BOOKS FOR STUDY:1. Ardilly, P and Yves T. (2006): Sampling Methods: Exercise and Solutions. Springer.2. Cochran, W.G. (2007): Sampling Techniques (Third Edition). John Wiley & Sons, New

Delhi.3. Desraj (1976): Sampling Theory. Tata McGraw Hill, New York.(Reprint 1979)4. Mukhopadyay, P. (2007): Survey Sampling. Narosa Publisher, New Delhi.5. Singh, D and Choudhary, F.S. (1977): Theory and Analysis of Sample Survey Designs.

Wiley Eastern Ltd, New Delhi.(Reprint 1986)6. Sukhatme, P.V. and Sukhatme, B.V. (1970): Sampling Theory Surveys with Applications

(Second Edition). Iowa State University Press.7. Sukhatme, P.V. and Sukhatme, B.V. (1958): Sampling Theory Surveys with Applications.

Indian Society of Agricultural Statistics, New Delhi.8. Thompson, S.K. (2012). Sampling. John Wiley & Sons.

1.5 ELECTIVE – I (shall be chosen from the list of Elective papers)

II SEMESTER

2.1 STATISTICAL INFERENCE – IUNIT I

Exponential family of distributions - Statistical decision problems – loss functions – 0-1 loss function - Absolute error loss function - Squared error loss function – Risk function – Minimax decision - Point estimation, interval estimation and testing of hypotheses as statistical decision problems - Point estimator – Choice of estimator – Amount of concentration - Mean squared error and variance - Sufficiency – factorization theorem – minimal sufficiency – completeness – ancillary statistic – Basu’s theorem.

UNIT II

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Unbiased estimator – Estimand – Estimable function –Rao-Blackwell’s theorem - uniformly minimum variance unbiased estimator – Lehmann-Scheffe’s theorem - Fisher’s information measure – Fisher’s information matrix - Lower bounds to variance of unbiased estimators - Cramer-Rao lower bound, - Bhattacharya’s lower bound - Chapman-Robbins lower bound - Applications of Cramer-Rao lower bound to the simultaneous estimation in bivariate normal distribution.

UNIT IIIMethods of estimation – Method of moments - method of minimum χ2 - method of

modified minimum χ2 - Likelihood function and its plotting – method of maximum likelihood (asymptotic properties of maximum likelihood estimators are not included) – method of scoring and Newton-Raphson’s method - Natural conjugate priors and Jeffreys non-informative prior – Bayes estimators under squared error loss function – Bayes risk.

UNIT IVConsistent and consistent asymptotically normal estimators – consistency of estimators by

the method of moments and the method of percentiles - Asymptotic properties of maximum likelihood estimators - Consistent asymptotically non-normal estimators - Information lower bound for asymptotic variance - Asymptotic relative efficiency.

UNIT VInterval estimation – confidence co-efficient and confidence interval – duality between

acceptance region and confidence interval – pivotal quantity method - large sample method - confidence belt - Chebyshev’s inequality and their applications - Shortest length confidence interval - Most accurate and uniformly most accurate confidence intervals - Construction of confidence intervals for population proportion (small and large samples) and difference between two population proportions (large samples) – confidence intervals for mean and variance of a normal population – confidence intervals for difference between means and ratio of variances of two normal populations.

Resampling methods – Bootstrap and Jacknife – simple problems.

BOOKS FOR STUDY:1. Berger, J.O. (1985): Statistical Decision Theory and Bayesian Analysis (Second Edition).

Springer Verlag, New York.2. Casella, G., and Berger, R.L. (2002): Statistical Inference (Second Edition). Thompson

Learning, New York. (Reprint, 2007).3. Goon, A.M., Gupta, M.K., and Dasgupta, B (1989): An Outline of Statistical Theory, Vol.

II, World Press, Kolkata.4. Kale, B.K. (2005): A First Course in Parametric Inference (Second Edition).Narosa

Publishing House, New Delhi. (Reprint, 2007).5. Keith Knight (2000): Mathematical Statistics. Chapman & Hall/CRC, New York.6. Lehmann, E.L., and Casella, G. (1998): Theory of Point Estimation (Second Edition).

Springer Verlag, New York. (Reprint, 2008).7. Mood, A.M., Graybill, F.A., and Boes, D.C. (1974): Introduction to theory of Statistics

(Third Edition). McGraw-Hill International Editions. 8. Rajagopalan, M. and Dhanavanthan, P. (2012): Statistical Inference. PHI Learning Pvt.

Ltd., New Delhi.9. Rao, C.R. (1973): Linear Statistical Inference and Its Applications (Second Edition).Wiley

Eastern Ltd., New Delhi.10. Rohatgi, V.K. and Saleh, A.K.Md.E. (2011): An Introduction to Probability and Statistics

(Second Edition). John Wiley & Sons, New York.

2.2 STOCHASTIC PROCESSES

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UNIT IIntroduction of stochastic processes - Specifications of a stochastic processes -

Classification of stochastic processes according to state space and time domain - Markov chains -Classification of states and chains - Higher transition probabilities and its limiting behavior -Chapman Kolmogorov’s equations - Stationary distribution - Ergodic theorem - One dimensional random walk and Gambler’s ruin problems.

UNIT IIContinuous time Markov processes - Poisson processes and related distributions - Birth and

death processes - Kolmogorov Feller differential equations of birth and death processes - Applications to queues and storage problems and Wiener process as a limit of random walks.

UNIT IIIStationary processes - Weakly stationary and strongly stationary processes - Properties of

auto covariance and auto correlation functions - Autoregressive and Moving average processes - Spectral density function - Spectral representation of moving average processes.

UNIT IVRenewal theory - Renewal equation - Stopping time - Wald’s equation - Elementary

renewal theorem and its applications - Renewal reward processes - Residual and Excess life times - Markov renewal and Semi Markov processes.

UNIT VBranching processes - properties of generating functions of Branching processes -

Probability of ultimate extinction - Limit theorems for continuous time branching process - Martingales in discrete time - Supermartingales and submartingales, Martingale convergence theorem and its applications.

BOOKS FOR STUDY:1. Cinlar, E. (2013): Introduction to Stochastic Processes, Courier Dover Publications2. Cox, D.R. and A.D. Miller (1984): The Theory of Stochastic Processes, Chapman & Hall.3. Harris, T.E. (1963): Theory of Branching Processes, Courier Dover Publications (Reprint

2002).4. Karlin, S. and Taylor, H.M (1975): A First Course in Stochastic Processes – Vol. I.

Academic Press, New York.5. Linda J.S. Allen (2011). An Introduction to Stochastic Processes with Applications to

Biology, Second Edition, Chapman & Hall/CRC.6. Medhi, J. (1984): Stochastic Processes, New Age International Publishing Limited, New

Delhi. (Reprint 2002).7. Papoulis, A. and Pillai, U.S. (2006). Probability, Variables and Stochastic Processes (Fourth

Edition). Tata McGraw-Hill.8. Resnick, S. (1992): Adventures in Stochastic Processes, Birkhauser, Boston. (Reprint 2005). 9. Ross, S.M (1996): Stochastic Processes, 2nd Edition, John Wiley & Sons, New Delhi.10. Tjims, H.C. (2003): A First course in Stochastic Models, John Wiley & Sons, New Delhi.

2.3 STATISTICAL QUALITY CONTROL AND RELIABILITY

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UNIT I Meaning and scope of statistical quality control - causes of quality variation - Control

charts for variables and attributes - rational subgroups - construction and operation of x̄ , σ, R, np, p, c and u charts - operating characteristic curves of control charts.

Modified control charts - basic principles and design of cumulative charts - V-mask.

UNIT II Moving-average and geometric moving-average control charts - sloping control chart.

Process capability analysis using histogram, probability plotting and control chart - Process capability ratios- use and their interpretations.

UNIT III Acceptance sampling - lot formation – sampling inspection by attributes – single

sampling plans – OC function – rectifying inspection - Double and multiple sampling plans – OC, ASN, ATI and AOQ functions - Use of Dodge – Roming and other tables of plans. AQL, LTPD, producer's risk and consumer's risk on OC curve - operation and use of single, double and multiple sampling plans.

Sampling inspection by variables - known and unknown sigma variables sampling plan - merits and demerits of variables sampling plan - derivation of OC curve and the parameters of the plan.

UNIT IV Continuous sampling plans by attributes - CSP-1 and its modifications - concept of

AOQL in CSPs - Multi-level continuous sampling plans - Operation of multi-level CSP of Lieberman and Solomon - Wald-Wolfowitz continuous sampling plans - Sequential Sampling Plans by attributes - OC and ASN functions.

UNIT VConcept of reliability, components and systems, coherent systems, reliability of coherent

systems - Life distributions, reliability function, hazard function, hazard rate, failure rates, common life distribution - exponential, Weibull, gamma distributions - Estimation of parameters -IFR and DFR distributions - Reliability of system with independent components - Basic idea of maintainability - Censoring and life testing, series and parallel systems.

BOOKS FOR STUDY:1. Barlow, R.E. and Proschan, F. (1981): Statistical theory of Reliability and Life testing:

Probability Models (Second Edition). To Begin With.2. Bowker, A.H and Lieberman, G.J. (1982): Engineering Statistics (Second Edition).

Prentice Hall, New Delhi, 3. Duncan, A.J. (2003.): Quality Control and Industrial Statistics, Irwin-Illinois. 4. Grant, E.L and Leavenworth, R.S. (2000): Statistical Quality Control (Seventh Edition),

Tata McGraw Hill, New Delhi. 5. Juran, J.M. and De Feo, J.A. (2010): Juran’s Quality control Handbook – The Complete

Guide to Performance Excellance (Sixth Edition). Tata McGraw-Hill, New Delhi.6. Mahajan, M. (2002): Statistical Quality Control (Third Edition), Dhanpat Rai and Co.,

Delhi. 7. Montgomery, D.C. (2009): Introduction to Statistical Quality Control (Sixth Edition),

Wiley India, New Delhi.8. Schilling, E. G. and Nuebauer, D.V. (2009): Acceptance Sampling in Quality Control

(Second Edition), CRC Press, New York.

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9. Wetherill, G.B. (1977): Sampling Inspection and Quality Control (Second Edition), Chapman and Hall, London.

2.4 OPERATIONS RESEARCHUNIT I

Linear Programming Problem (LPP) - Definitions of Feasible solution (f.s.), basic feasible solution(BFS) - optimal solution - Standard form - Simplex method: Theory and algorithm - Charne’s M-technique and Two-phase method - Duality in LPP: Principle of duality and related results - Dual simplex method - Sensitivity analysis - Discrete changes in the cost vector c and requirement vector b - Integer Programming Problem (IPP) - Need for IPP and types - Gomory’s cutting plane algorithm for all IPP.

UNIT II Transportation Problems - Mathematical formulation, Basic Feasible Solution (BFS) - Loops

in a transportation problem and their properties – Methods of BFS and test of optimality - Transportation Algorithm - Degeneracy in transportation problem - Unbalanced transportation problem - Assignment Problem – Introduction and Mathematical Formulation - Hungarian Method - Unbalanced Assignment Problem.

UNIT III Game Theory - Two-person zero-sum games – Maxmin - Minimax Criterion - Minimax and

Saddle point Theorem - Principle of Dominance - Connection between Game problem and LPP - Solution of (m x n) games - Algebraic method and Matrix method - Iterative method for approximate solution.

UNIT-IVProject Management by PERT and CPM: Meaning of PERT and CPM - Basic steps

involved in PERT/ CPM techniques - Network diagram representation - Fulkerson’s rule of drawing a network diagram - Determination of critical path, project duration and crushing of project duration – PERT- time estimates and related results - Determination of critical path, estimate of project duration.

UNIT-V Queueing models – Queueing system – Queueing problem - Definition of transient and

Steady-states - Kendall’s notations and classification of queuing models - Distributions in queuing systems - Solution of queuing models: Model I: (M/M/1:/FCFS): Birth and Death Model. Inter-relationship between Lq, Ls, Wq and Ws: Model-II - General Erlangian queuing model (Birth-Death Process) - Model-III: (M/M/1: N/FCFS) and Model IV: (M/M/S//FCFS) - Steady-state solutions of Markovian queuing models of M/M/1, M/M/C and M/G/1 with limited waiting spaces.

BOOKS FOR STUDY:1. Gass, S.I. (1985): Linear Programming, Methods and Applications. Courier Dover

Publications. (Reprint 2003)2. Gupta, P.K. and Man Mohan. (1979): Operations Research: Linear Programming and

Theory of Games (3rdEdition). Sultan Chand and Sons, New Delhi.3. Hadley, G (1963): Linear Programming. Addison Wesley Publishing Company.4. Hillier, F.S. and Lieberman, G.J. (2005): Introduction to Operations Research (9 th Edition).

McGraw – Hill Publishing Company.5. Sharma, J.K. (2013): Operations Research: Problems and Solutions (Fifth Edition).

Macmillan India Limited.6. Sharma, S.D (2010): Operations Research. Kedar Nath Ram Nath and Co, Meerut.

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7. Swarup, K., Mohan, M. and Gupta P.K. (2001): Operations Research. Sultan Chand and Sons, New Delhi.

8. Taha, H.A (2011): Operations Research: An Introduction (9th Edition). Prentice Hall Publishing Company.

2.5 SUPPORTIVE COURSE – I

(Supportive Course –I shall be chosen from the list of Supportive Papers)

2.6 STATISTICS PRACTICAL USING SOFTWARE – I

III SEMESTER

3.1 STATISTICAL INFERENCE – IIUNIT I

Testing of hypotheses – fundamentals of hypotheses testing – randomized and nonrandomized tests - Most powerful test – Neyman-Pearson’s fundamental lemma - Monotone likelihood ratio property – uniformly most powerful test - Applications to standard statistical distributions.

UNIT II Generalization of Neyman-Pearson fundamental lemma (statement only) - Unbiased tests –

construction of uniformly most powerful unbiased tests for one-parameter and multi-parameter exponential family of distributions – applications to standard statistical distributions - Similar tests – Neyman structure - Locally most powerful and locally most powerful unbiased tests.

UNIT IIIInvariance – maximal invariant statistic – invariant test - Likelihood ratio test – asymptotic

distribution of likelihood ratio test statistic – consistency of likelihood ratio test – construction of likelihood ratio tests for standard distributions - analysis of variance (one-way method) – Bartlett’s test for homogeneity of variances.

UNIT IVU statistic and its properties.

One-sample tests - tests for goodness of fit – χ2 and Kolmogorv-Smirnov tests - tests for randomness – runs test - sign test and Wilcoxon’s signed rank test. Two-sample tests - Kolmogov-Smirnov’s test - Mann-Whitney U test, median test. K-sample tests – Kruskal-Wallis test and Friedman’s test.

UNIT VNeed for sequential procedures in statistical inferential problems. Sequential probability

ratio test – approximation to stopping bounds – Wald’s fundamental identity (statement only) – operating characteristic and average sample number functions – applications to standard distributions – Termination property.

BOOKS FOR STUDY:1. Casella, G. and Berger, R.L. (2002): Statistical Inference (Second Edition). Thompson

Learning, New York. (Reprint, 2007).2. Conover, W.J. (1999): Practical Nonparametric Statistics (Third Edition). John Wiley &

Sons, New York. (Reprint, 2007).

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3. Ghosh, B.K. (1970): Sequential Tests of Statistical Hypotheses. Addison-Wesley, New York.4. Gibbons, J.D. and S. Chakraborti. (2010): Nonparametric Statistical Inference (Fifth Edition).

Taylor & Francis, New York.5. Goon, A.M., Gupta, M.K. and Dasgupta, B. (1989): An Outline of Statistical Theory, Vol.II.

World Press, Kolkata.6. Kale, B. K. (2005): A First Course in Parametric Inference (Second Edition). Narosa

Publishing House, New Delhi. (Reprint, 2007).7. Keith Knight (2000): Mathematical Statistics. Chapman & Hall/CRC, New York.8. Lehmann, E. L. and Romano, J.P. (2005): Testing Statistical Hypotheses (Third Edition),

Springer Verlag, New York. (Reprint, 2009).9. Rao, C. R. (1973): Linear Statistical Inference and Its Applications (Second Edition), Wiley

Eastern Ltd., New Delhi.10. Rohatgi, V. K. and Saleh, A.K.Md.E. (2001): An Introduction to Probability and Statistics

(Second Edition). John Wiley & Sons, New York. (Reprint, 2009).11. Rajagopalan, M. and Dhanavanthan, P. (2012): Statistical Inference. PHI Learning Pvt. Ltd., New Delhi.

3.2 MULTIVARIATE ANALYSISUNIT I

Singular and non-singular Multivariate normal distributions and their properties - Marginal and conditional distributions - Characteristic function and moments - Distribution of linear combinations of multivariate normal vector - Determination of mean and variance -covariance matrix of multivariate normal distribution.

UNIT IIRandom Sampling from multivariate normal distribution - Maximum likelihood estimators

of the parameters of multivariate normal distribution - distribution of sample mean vector and sample dispersion mean vector - Necessary and sufficient condition for a quadratic form to be distributed as chi-square - Inference concerning the sample mean vector when covariance matrix is known.

UNIT IIIGeneralized T2 statistic and its distribution - Hotelling's T2 statistic and its distribution - Two

sample problems with unequal covariance matrices likelihood ratio criterion and its applications - Mahalanobis D2 statistic and its distribution - Applications of Hotelling’s T2 Statistic - Invariance property of T2 statistic - Relationship between T2 and D2 statistics - Behrens–Fisher Problem.

UNIT IVWishart distribution - Sampling distribution of sample covariance matrix - Properties of

Wishart distribution - Wilk’s criterion - Generalized variance (Concept only) - Sampling distribution of simple sample correlation coefficient - Sampling distribution of partial and multiple correlation coefficients in null case (without derivation) - Tests concerning simple, partial and multiple correlation coefficients - Discriminant function (concept only) - Fisher’s discriminant function.

UNIT VProblem of classification - Two populations and k populations - Principal components and

their determination - Factor analysis – estimation of factor loadings - Canonical variables and canonical correlations - Derivation of canonical correlation coefficients.

BOOKS FOR STUDY:

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1. Anderson, T.W. (2003): An Introduction to Multivariate Statistical Analysis (Third Edition). Wiley–Inter science, New York.

2. Johnson, R.A. and D.W. Wichern. (2013). Applied Multivariate Statistical Analysis (Sixth Edition), Pearson New International Edition.

3. Kendall, M.G., Stuart, A. and Ord, K.J. (1973): The Advanced Theory of Statistics. (Fourth Edition), Vol. 2, Charles Griffin company Ltd.

4. Kotz, S., Balakrishnan, N. and Johnson, N.L. (2000): Continuous Multivariate Distribution Models and Applications (Second Edition). Vol. 1, Wiley-Inter science, New York.

5. Mardia, K.V., Kent, J.T and Bibby, J.M. (1979): Multivariate Analysis. Academic Press,

New York.6. Morrison, D.F. (2004): Multivariate Statistical Methods (Fourth Edition). Duxbury Press,

New York.7. Rao, C.R. (2001): Linear Statistical Inference and its Applications (Second Edition).

Wiley-Inter Science, New York.8. Rencher, A.C. (2002): Methods of Multivariate Analysis (Second Edition). Wiley-

Interscience, New York.

3.3 ECONOMETRICSUNIT I

Nature and scope of Econometrics - Illustrative examples Production and cost analysis - Theory and analysis of consumer demand specification - Estimation of demand function - Price and income elasticity of demand - Price elasticity’s of supply - Torquivists model of demand for inferior goods models building bias in construction of models.

UNIT IISingle equation linear model static case - Ordinary least square model and generalized least

squares model: Introduction - estimation and prediction - Problem of multicollinearity and heteroscedasticity – Causes, consequences and solutions of and estimation.

UNIT III

Autocorrelation: Causes, consequences and testing for auto-correlated disturbances - Autoregressive series of order 1 (AR(1)) - Lagged variables and distributed log methods - Errors in variable models and Instrumental variables. Economical Forecasting – long term and short term.

UNIT IVSimultaneous equations model- Concept, structure and types - Identification Problem with

restrictions on variance and covariance - Rank and order conditions of identifiability –Methods of estimation- Indirect least square method, two-stage least squares method of estimation and Estimation of Limited Information Maximum Likelihood (LIML).

UNIT V K-Class estimators - Full information estimators - Full Information Maximum Likelihood

(FIML) - Three stage least squares estimators (3-SLS) and its Properties - Comparison of various estimation methods.

BOOKS FOR STUDY:1. Castle, J. and Shephard, N. (2009). The Methodology and Practice of Econometrics. OUP

Oxford publications.2. Gujarati, D.N. and Sangeetha (2007). Basic Econometrics (Third Edition). McGraw Hill

Publisher, New York. 3. Goldberger, A.S. (1964): Econometrics theory. John Wiley & Sons, New Delhi.

15

4. Kelejion, H. H. and Oates, W.E. (1988). Introduction to Econometrics, Principles and Applications. Harper and Row Publishers Inc., New York.5. Maddala, G.S. and Kajal Lagari (2009). Introduction to Econometrics. John Wiley & Sons.6. Madnani, G.M.K. (2008): Introduction to Econometrics: Principles and Applications.

Oxford and IBH Publishing.7. Wooldridge, J. (2012). Introduction Econometrics: A Modern Approach. Cengage Learning.

3.4 DEMOGRAPHYUNIT I

Development and scope of demography - Demographic data: sources and current status - Chandrashekar-Deming index - Adjustment of age data – use of Whipple – Myer and UN indices - Population size and growth in India - Trends and differentials in world population – Health Surveys and use of hospital statistics – Population transition theory.

UNIT II Mortality - Basic measurements - Crude, specific, standardized death rates - Life

table - construction, use and interpretation - force of mortality - abridged life tables.

UNIT III Fertility -Basic measurements - Gross and Net Reproduction rate - Cohort fertility

analysis - Fertility models - Population regulation programs in India - Demographic transition theory.

UNIT IV Special distribution of population - basic concepts - measurements and models of

migration - concept of international migration - Urban development components of urban and metropolitan growth - Urbanization in developed and developing countries - Stable and quasi populations- Intrinsic growth rate.

UNIT V Components of population growth and change – Models of population growth and their

filling to population data - Methods of projection - Logistic equation - component method of projection - stable population theory – Decennial population census in India – Nuptiality and its measurements.

BOOKS FOR STUDY:1. Benjamin, B. (1975): Demographic Analysis. George Allen and Unwin Limited.2. Bogue, D.J. (1969). Principles of Demography. Digitized 20073. Cox, P.R. (1978): Demography (Fifth Edition). Cambridge University Press.4. Gibbs, J.P. (2012). Urban Research Methods. Literary Licensing, LLC.5. Keyfliz, N. and Caswell, H. (2006). Applied Mathematical Demography. Springer. 6. Kumar, R. (1986): Technical Demography. John Wiley & Sons, Canada.7. Misra, B.D. (1982). An Introduction to the Study of Population. South East Asia Publishers,

Madras.8. Spiegelman, M. (1969): Introduction to Demographic Analysis. Harvard University Press. 9. Wolfenden, H.H. (1954). Population Statistics and their Compilation. Am Actuarial Society.

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3.5 LINEAR MODELS AND DESIGN OF EXPERIMENTS UNIT I

Linear models – assumptions on error components – Fixed, Random and mixed effects models, models with full rank and less than full rank - least square and maximum likelihood estimators of the parameters and their properties - Gauss-Markov theorem - testing linear hypotheses.

UNIT IIAnalysis of variance for one-way, two–way classification with one and more than one

(equal) observations per cell with interaction - Multiple comparisons: Fisher’s least significance difference (L.S.D.) test and Duncan’s Multiple Range test (DMRT) - Analysis of covariance (ANCOVA) - description of the method in the case of one and two concomitant variables - analysis of mixed plot data, three way concomitant.

UNIT III Fundamental principles of design of experiments - Randomization, Replication and

Local control - Completely randomized design (CRD) - Randomized block design (RBD) - Latin square design(LSD) and their analyses - Missing plot technique for RBD and LSD - more than one observation per cell in RBD -Graeco-LSD-ANACOVA technique in CRD,RBD and LSD - Transformations.

UNIT IV Factorial experiments - 24

and 33 experiments and their analysis - complete and partial confounding, their construction - Analysis in 24 and 33 experiments - Fractional replication in 24

and 33 experiments - Construction and their analysis - concept of asymmetrical factorial experiments - Split-plot and Strip-plot designs.

UNIT VIncomplete block design - Balanced incomplete block design and partially balanced

incomplete block design with two associate classes-parametric relation and analysis - Youden square design- concept and analysis - Concept of Lattice design - Analysis of non-orthogonal data.

BOOKS FOR STUDY:1. Cochran, W. G and Cox, G. M. (1957): Experimental Design. John Wiley & sons, New

York.2. Das, M. N. and Giri, N. S. (1986): Design and Analysis of Experiments (2nd Edition). Wiley

Eastern Ltd., New Delhi.3. Dey, A. (2010): Incomplete Block Design. World Scientific Publishing Company.4. Fisher, R. A. (1953): Design and Analysis of Experiments. Oliver and Boyd, London.5. Giri, N.C. (1986): Analysis of Variance. South Asian Publisher, New Delhi.6. John, P.W.M (1998): Statistical Design and Analysis Experiments. Macmillan Company,

New York.7. Joshi, D.D (1987): Linear Estimation and Design of Experiments. New Age International

(P) Ltd. New Delhi.8. Kempthorne, O. (1976): Design and Analysis of Experiments. John Wiley & Sons, New

York.9. Montgomery, D.C. (2012). Design and analysis of Experiments. John Wiley & Sons, New

Delhi.10. Searle, S.R. (2012). Linear Models. John Wiley & Sons, Inc., New York.11. Shan, S.M. and Kabe. (1983). An Introduction to Construction and Analysis of Statistical

Designs (Issue 64). Queen University Publications.

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3.6 SUPPORTIVE COURSE – II

(Supportive Course –II shall be chosen from the list of Supportive Papers)

IV SEMESTER

4.1., ELECTIVE PAPERS (shall be chosen from list of Elective papers)

4.2., ELECTIVE PAPERS (shall be chosen from list of Elective papers)

4.3., ELECTIVE PAPERS (shall be chosen from list of Elective papers)

4.4. STATISTICS PRACTICAL USING SOFTWARE - II

SYLLABUS FOR ELECTIVE PAPERS

ELECTIVE – I: PROGRAMMING IN C++ AND S-PLUS/RUNIT I

Principles of Objects Oriented Programming –Software Crisis – Software Evolution – Procedure Oriented Programming – Object Oriented Programming paradigm – Basic concepts and benefits of OOP – Structure of C++ - Manipulators.

UNIT II Functions in C++ : Functions prototyping – Call by Reference – Return by Reference – In

– line function – Default, Const Arguments –Functions Overloading – Friend and Virtual Functions – Classes and Objects - Member functions – Nesting of Member functions – Private member functions – Memory allocation for objects – Static data members – Static member function – Returning Object – Const Member Function – Pointers to members.

UNIT III Constructors: Parameterized Constructors – Multiple Constructors in C Classes –

Constructors with Default Arguments – Dynamic – Initialization of Objects – Copy and Dynamic Constructors – Destructors - Operator Overloading – Unary and Binary Operators – Overloading Binary Operators using Friend Functions.

UNIT – IVIntroduction – Import the data set – Summarize the data – Data objects and manipulation -

Fit a linear regression model – Graph the model fit – Exporting data in various formats (text, Excel, Access) - Managing multiple projects.

UNIT – VConcepts for Programming with R – Objects – Basic data and Computations – Data input –

Data frames – Graphics – Tables – Statistical Modeling.

BOOKS FOR STUDY:1. Balagurusamy, E. (2001): Object oriented Programming with C++ (2nd Edition). Tata

McGraw Hill Publishing Company Limited.2. Crawly, M.J. (2012). The R book (Second Edition). John Wiley & Sons.3. Dalgaard, P. (2008). Introductory Statistics with R. Springer Verlag Inc.,4. Drăghici, S. (2011). Statistics and Data Analysis for Microarrays Using R and Bioconductor

(Second Edition). CRC press.18

5. Everitt, B.S. (2001). A Handbook of Statistical Analyses Using S-Plus (Second Edition). CRC Press.

6. Lafore, R. (1995): Object Oriented Programming with C++. Tata McGraw Hill Publishing Company Limited.

7. Logan, M. (2011). Bio statistical Design and Analysis Using R: A Practical Guide. John Wiley & Sons.

8. Stroup, B. (1991): The C++ Programming Language, Addison Wesley.

ELECTIVE - I: PROGRAMMING IN VISUAL BASICUNIT I

Fundamental of VB: Anatomy of VB program - The code window - Statements in VB - Assignment and property setting - Variables - Strings-Numbers, Constants, repeating operations, making decisions.

UNIT II Working with objects at time - projects with multiple forms - Displaying information -

The printer object - Advanced programming techniques - Arrays pointer - Built in function - User defined functions and procedures.

UNIT III Objects - Manipulation of Objects in VB - Collections - Creating an object in VB -

Building - Files - Sequential files - random access files - Binary files - Sharing files.

UNIT IV Communicating with other windows application: Clip board activity windows

applications - Dynamic data exchange and OLE 2.

UNIT V Data base features: Modern database - data manager - using the data control -

programming with data control - monitoring change to the database - SQL basics objects.

BOOKS FOR STUDY:1. Programming in Visual Basic. Tech media, BPB Publication, New Delhi.2. VB4: Nuts and Bots for Experienced programmers.3. VB5: Steve Brown BPB Publications.4. VB5: Interactive Course Tech Media Waite Group.5. VB56: Series, Tech Media Waite Group.6. VISUAL BASIC 6: The Complete Reference with CD.

ELECTIVE- I: COMPUTER SIMULATION AND MODELLINGUNIT I

Introduction to Simulation: Advantages and Disadvantages of Simulation - Areas of Application - System Environment - Components of a system - Types of models - Discrete-event system simulation -Steps in a Simulation Study; Simulation examples - Programming Languages for simulation: FORTRAN,GPSS,SIMAN,SIMSCRIPT, SLAM and MODSIM III.

UNIT II Statistical Models in Simulation: Useful Statistical model - Discrete Distribution -

Continuous Distribution - Poisson Process - Empirical Distribution. Simulation of Manufacturing and Material Handling System: Modeling of manufacturing system - Models of martial Handling system - Goals and performance Measure - Issues in Simulating Manufacturing and Material Handling system - Simulations and Languages for Manufacturing and Material handling system.

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Simulation of Queuing system: Queuing system Characteristics - Queueing Notation - Transient and Steady-State Behaviour of Queues - Long-Run Measure of Performance of Queueing system - Steady-state Behaviour of Infinite-Population Markovian Models - Network of Queues.

UNIT III Random-Number Generation :Properties of Random Numbers Generation of Pseudo-

Random Numbers-Techniques for generating Random Variate Generation: Inverse Transformation Technique - Uniform Distribution, Exponential Distribution, Triangular Distribution, Empirical Continuous Distribution- Discrete Distribution - Direct Transformation for the Normal Distribution - Convolution method for Erlang Distribution - Acceptance-Rejection Technique: Poisson Distribution - Gamma Distribution.

UNIT IV Input Data Analysis: Data Collection - Identifying the Distribution with Data -

Parameter Estimation - Goodness-of fit Tests- Chi-square Test- Kolmogorov - Smirnov Test - Selecting Input models without Data - Multivariate and Time Series - Input Models.

Verification and Validation of Simulation Models: Model Building - Verification and Validation - Verification of Simulation models - Calibration and Validation of models: Face Validity - Validation of model Assumptions - Validations Input-Output Transformations - Input-Output Validation using Historical Input Data - Input-Output Validation using a Turing Test.

UNIT V Output Data Analysis: Stochastic Nature of Output Data - Types of Simulation with

respect their Estimation - Output Analysis for Terminating Simulation - Output Analysis for Steady - State Simulations.

Comparison and Evaluation of Alternative System Designs: Comparison of Two system Design - Comparison of several systems Design - Statistical models for estimating the Effect of Design Alternative – Meta modeling.

BOOKS FOR STUDY:1. Deo, N. (1983): System Simulation with Digital Computer. Prentice Hall of India (Digitized

2007)2. Gardon, G. (1992): System Simulation (Second Edition). Prentice Hall of India.3. Jerry Banks, John S. Carson, II and Barry L. Nelson. (1995). Discrete - Event System

Simulation (Second Edition). Prentice Hall.4. Law, A.M. (2007). Simulation Modeling and Analysis (Fourth Edition). McGraw Hill

Education.

ELECTIVE- I: DATA MININGUNIT I

Introduction: Data mining - Kinds of data – Data mining Functionalities - Classification of Data mining Systems - Major Issues on Data mining - Introduction to OLAP - OLAP technology for Data Mining - Data warehousing - Data warehousing to Data mining - Optimizing Data for mining - Data preprocessing.

UNIT IIData Mining Primitives: Data mining Query language - Association Rules in large - Data

mining - KDD Process - Fuzzy sets and logic - Classification and Prediction: Information retrieval - Dimensional Modeling of Data - Pattern Matching - Estimation Error- EM and MLE.

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UNIT IIIModels based on Summarization: Bayes Theorem - Chi squared Statistics Regression -

Decision Tree - Neural Networks - Genetic Algorithms - Cluster Analysis – Outlier - Cluster Vs Classification - Clustering Issues - Impact of Outliers on clustering- Clustering problems - Clustering Approaches.

UNIT IVClustering Algorithms: Hierarchical algorithm – Single Link- MST Single Link - Complete

Link - Average Link- Dendrogram - Partitional Algorithm – MST - Squared Error - K-Means - Nearest Neighbor – PAM – BEA – GA - Categorical algorithm - Large Database.

UNIT V Web Mining: Introduction - Web data - Web Knowledge Mining Taxonomy - Web Content

mining - Web Usage Mining Research - Ontology based web mining Research - Web mining Applications.

BOOKS FOR STUDY:1. Berry, J.A. and Linoff, G.S. (2011): Data Mining Techniques (Third Edition). John Wiley &

Sons. 2. Chattamvelli, R. (2009): Data mining Methods. Alpha Science International. 3. Dunham, M.H. (2006): Data mining: Introductory and Advanced Topics. Pearson Education

India.4. Gorunescu, F. (2010): Data mining Concepts, Models and Techniques. Springer.5. Han, J. and Kamber, M (2001): Data mining Concepts and Techniques (Seventh Edition).

Morgan Kaufmann Publications.6. Hand, D., Mannila, H. and P. Smyth (2001): Principles of Data mining. MIT press.7. Larose, D.T. (2005): Discovering Knowledge in Data: An Introduction to Data mining. John

Wiley & Sons, Canada.8. Pujari, A.K. (2001): Data mining Techniques, Universities press.9. Sivanandam S.N. and S. Sumathi (2006): Data mining Concepts, Tasks and Techniques,

Springer.

ELECTIVE – II: APPLIED REGRESSION ANALYSISUNIT I

Regression and outliers: Introduction and review of basic results on regression - Drawing conclusions - Interpreting estimates - Case analysis, residual and influence, symptoms and remedies - Data analysis approach to residual analysis including Box-Cox transformation - Identification of outliers - Identification of leverage points - Cook's D, DFFITS and DFBETAS methods – Measures of Model performance - Detecting and Treatment of Influential Observations.

UNIT II Regression and Collinearity: Tools for handling multi-collinearity - Methods based on

singular value decomposition and ridge regression - Properties of ridge estimator.

UNIT III Introduction to general non-linear regression - Least squares in nonlinear case -

Estimating the parameters of a nonlinear system - Reparameterization of the model - Geometry of linear and nonlinear least squares - Nonlinear growth models.

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UNIT IV Generalized Linear Models: Introduction - Analysis of Binary model - Logistic

Regression Models - Log linear Models – Link functions and linear predictors – Parameter estimation and Inference in the GLM – Prediction and Estimation with the GLM - Residual Analysis in the GLM and over dispersion.

UNIT V Introduction to Bootstrap methods: parametric - non-parametric Bootstrap- their

important properties (without proof).

BOOKS FOR STUDY:1. Barnett, V. and T. Lewis. (1994): Outliers in Statistical Data (Third Edition). John Wiley &

Sons, New York. (Digitized 2009).2. Belsley, D.A., Kuth, E. and Welsch, R.E. (2004): Regression Diagnostics- Identifying

Influential Data and Sources of Collinearity. John Wiley & Sons, New York.3. Chatterjee, S. and Hadi, A.S. (2012): Regression Analysis by Examples. John Wiley &

Sons, New York.4. Cook, R.D. (1979) Influential Observations in Linear Regression. Journal of American

Statistical Association, Vol: 74, pp. 169-174.5. Cunst, R.F., and R.L. Mason. (1980): Regression Analysis and Its Applications-A data

Oriented Approach. Marcel Dekker Inc., New York. 6. Daniel, C. and F.S. Wood. (1999): Fitting Equations to Data (Second Edition), John Wiley

& Sons, New York.7. Draper, N.R, and H. Smith. (1998): Applied Regression Analysis (Third Edition). John

Wiley & Sons, New York.8. Dramer, N.R, and J.A. John. Influential Observations and Outliers in Regression,

Technometrics, Vol: 23 pp 21.9. Hocking, R.R. and Pendleton, O.J. (1983). The Regression Dilemma. Communications in

Statistics - Theory and methods, Vol: 12, pp 497-527. 10. Myers, R.H., Montgomery, D.C., Vining, G.G. and Robinson, T.J. (2012): Generalized Models: with Applications in Engineering and the Sciences (Second Edition). John Wiley & Sons.

ELECTIVE - II: RELIABILITY THEORY AND ITS APPLICATIONSUNIT I

Reliability concepts and measures – components and systems – Coherent systems and their reliability – cuts and paths – modular decomposition – bounds on system reliability – structural reliability importance of components.

UNIT IILife time distributions – reliability function – hazard rate - common life time distributions

– exponential, gamma, normal, Weibull, Rayleigh etc. – estimation of parameters and testing of hypotheses in these distributions.

UNIT IIINotions of ageing – IFR, IFRA, NBU, DMRL and NBUE classes and their duals –

implications – closures of these classes under formation of coherent systems.

UNIT IVReliability estimation based on failure times under various censored life tests and tests with

replacement of failed items – stress-strength reliability and its estimation.

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UNIT VReliability growth models – probability plotting techniques – Hollander-Proschan and

Deshpande tests for exponentiality – tests for HPP vs NHPP with repairable systems - Basic ideas of accelerated life testing.

BOOKS FOR STUDY:1. Bain, L.J. and Engelhardt. (1991): Statistical Analysis of Reliability and Life Testing

Models. CRC Press.2. Barlow, R.E., and Proschan, F. (1981): Statistical Theory of Reliability and Life Testing

(Second Edition). Holt, Rinehart and Winston, New York.3. Blischke, W.R. and Murthy, D.N.P. (2000): Reliability–Modeling, Prediction and

Optimization. John Wiley & Sons, New York.4. Lawless, J.F. (2011): Statistical Models and Methods for Lifetime Data (Second Edition).

John Wiley & Sons, 5. Nelson, W.B. (2005): Applied Life Data Analysis. John Wiley & Sons, New York.6. Singpurwalla, N.D. (2006): Reliability and Risk – A Bayesian Perspective. John Wiley &

Sons, New York.7. Zacks, S. (2011): Introduction to Reliability Analysis. Springer London, Limited,

ELECTIVE- II: ADVANCED STATISTICAL QUALITY CONTROLUNIT I

Quality and Quality system: Quality, Quality improvement and productivity, specification and requirement - Quality characteristics, standard and measurements - Concepts of quality control, quality assurance, quality circle, quality system - Scope of quality control and quality system.

UNIT II Quality cost Analysis and Management: Prevention costs, Appraisal costs, Internal

failure costs External failure costs, Management of quality costs - Production quality control - product quality audit - quality information - Total Quality Management- Concepts and meaning - Meaning of acceptance quality control- Distribution between acceptance control and process control- concept of process quality control.

UNIT III Cumulative-Sum control charts: principle of CUSUM charts - Construction of

sample range and standard deviation - CUSUM charts for count of nonconformities and for number of non-conforming units - CUSUM procedures for large shifts and for initial response (FIR).

UNIT IV Exponentially Weighted Moving Average Charts: principle of acceptance control charts-

Modified control units- modified acceptance control charts - Choice between modified and acceptance control limits - Group control charts for multiple- stream process- Multivariate quality control charts.

UNIT V Acceptance Sampling: Sequential sampling plans by attributes and variables- Derivation

of OC and ASN function - Lot-sensitive sampling by plan(LSPs) - MIL-STD-105D -Description of the standard- Dodge-Roming sampling plans - Single and Double sampling LTPD and AOQL plans - Concepts of Tightened Normal tightened (TNT) sampling plans.

BOOKS FOR STUDY:1. Duncan, A.J. (2006): Quality Control and Industrial Statistics (Fifth Edition). Textbook

Publishers. 23

2. Grant, E.L. and Leavenworth, R.S. (2000): Statistical Quality Control (Seventh Edition). Tata McGraw-Hill Education.

3. Montgomery, D.C. (2009): Statistical Quality Control – An Introduction (Sixth Edition). Wiley India, New Delhi.

4. Schilling, E.G. and Neubauer, D.V. (2009): Acceptance Sampling in Quality Control (Second Edition): CRC Press, New York.

5. Wadswirth, H.M., Stephens, K.S. and Godfrey, A.B. (2004): Modern Methods for Quality Control Improvement. John Wiley & Sons, New York.

6. Whetherill, G.B. and Brown, D.W. (1995): Statistical Process Control- Theory and Practice. Chapman and Hall, London.

ELECTIVE- II: ACTUARIAL STATISTICSUNIT I

Mortality: Level, trend and differentials in mortality - forces of mortality - Gompetz and Makeham laws of mortality- Complete and abridged life tables-construction, interpretation - applications -stationary funds.

UNIT II Annuities: Pure endowments - Annuities – Accumulations – Assurances - Varying annuities

and assurances - Continuous annuities - family income benefits.

UNIT III Policy Values: Nature of reserve - prospective and retrospective reserves - fractional

premiums and fractional durations - modified reserves - Continuous reserves - Surrender values and paid up policies - Industrial assurance - Children's deferred assurances - Joint life and last survivorship.

UNIT IV Contingent Functions: Contingent probabilities - Contingent assurances - reversionary

annuities - multiple-decrement table - forces of decrement - construction of multiple decrement tables.

UNIT V Pension Funds: Capital sums on retirement and death- widow's pensions - Sickness benefits

- Benefits dependent on marriage.

BOOKS FOR STUDY:1. Barcley G.W. (1970): Techniques of Population Analysis. John Wiley, New York.2. Borowiak, D.S. and A. F. Shapiro. (2013). Financial and Actuarial Statistics: An

Introduction (Second Edition). CRC press.3. Donald, D.W.A. (1970): Compound interest and annuities (Second Edition). The Institute of

Actuaries and the Faculty of Actuaries at the University Press.4. Elandt -Johnson, R.C. and Johnson, N.L. (1999): Survival Models and Data Analysis. John

Wiley.5. King, G. Institute of Actuaries textbook, Part II, (Second Edition). Institute of Actuaries

(Great Britain). 6. Spurgeon, E.T. (2011): Life Contingencies (3rd Edition). Cambridge University Press.

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ELECTIVE- II: FUZZY LOGIC AND ITS APPLICATIONSUNIT I

Uncertainty and Imprecision – Statistics and Random Processes – Uncertainty in Information – Fuzzy Sets and membership – Chance versus Ambiguity - Classical Sets and Fuzzy Sets: Classical Sets – Fuzzy Sets – Sets as Points in Hyper-cubes - Classical Relations and Fuzzy Relations: Cartesian Product – Crisp Relations – Fuzzy Relations – Tolerance and Equivalence Relations – Fuzzy Tolerance and Equivalence Relations - Membership Functions. UNIT II

Fuzzy-to-Crisp Conversions: Lambda-Cuts for Fuzzy Sets – Lambda-Cuts for Fuzzy Relations – Defuzzification Methods - Fuzzy Arithmetic, Numbers, Vectors and the Extension Principle - Extension Principle – Fuzzy Numbers – Interval Analysis in Arithmetic – Approximate Methods of Extension – Fuzzy Vectors.

UNIT IIIClassical Logical and Fuzzy Logic: Classical Predicate Logic – Fuzzy Logic – Approximate

Reasoning – Fuzzy Tautologies, Contradictions, Equivalence, and Logical Proofs – Other Forms of the Implication Operation – Other Forms of the Composition Operation - Fuzzy Rule-Based Systems: Natural Language – Linguistic Hedges – Rule-Based Systems – Graphical Techniques of Inference.

UNIT IVFuzzy Nonlinear Simulation: Fuzzy Relational Equations – Partitioning – Nonlinear

Simulation Using Fuzzy Rule-Based Systems – Fuzzy Associative Memories (FAMs) - Fuzzy Decision Making: Fuzzy Synthetic Evaluation – Fuzzy Ordering – Preference and Consensus – Multi-objective Decision Making – Fuzzy Bayesian Decision Method – Decision Making under Fuzzy States and Fuzzy Actions.

UNIT VFuzzy Classification: Classification by Equivalence Relations – Cluster Analysis – Cluster

Validity – Classification Metric – Hardening the Fuzzy- Similarity Relations from Clustering. Fuzzy Pattern Recognition: Feature Analysis – Partitions of the Feature Space – Single Sample Identification – Multi-feature Pattern Recognition – Image Processing – Syntactic Recognition.

BOOKS FOR STUDY:1. George, A. and Anastassiou. (2010). Fuzzy Mathematics: Approximation Theory. Springer.2. George J. Klir and Tina A. Folge.(1988). Fuzzy Set, Uncertainty, and Information. Prentice-

Hall, Inc, USA.3. Klir, G.J. and B. Yuan. (1995). Fuzzy sets and Fuzzy logic Theory and Applications.

Prentice-Hall Inc., (Reprint 2003).4. Nanda. S and Das .N.R. (2010). Fuzzy Mathematical Concepts. Narosa Publishing House,

Pvt, Ltd, New Delhi 110002.5. Nguyen, H.T., Prasad, N.R., Walker, A.L. and Walker, E.A. (2003). A First Course in

Fuzzy and Neural Control. Chapman Hall/CRC press.6. Nguyen, H.T. and Walker, E.A. (2005). A First Course in Fuzzy Logic (Third Edition).

CRC Press.

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7. Ross, T.J. (2009). Fuzzy Logic with Engineering Applications (Third Edition). John Wiley & Sons.

8. Yen, J. and Langari, R. (1999). Fuzzy logic Intelligence, control and information. Prentice Hall.

ELECTIVE - III: DATA ANALYSIS USING SOFTWARE UNIT - I Introduction to SAS – Use Interface – Different types of windows and menus. SAS Language – program steps – Variable Names and Data Set Names. Variable lists. Creation of SAS data sets from Raw data – Data, Infile and Input statements. Reading data from other programs and database. Reading data from an existing SAS data set and modifying SAS data.

UNIT - II

Introduction to PROC, Var, Where, By, Class and Global statements. Graphics – xy; sg; summary and panel plots. The output Delivery System – ODS Procedure Output, ODS Styles, Saving output in SAS Data Sets – ODS out put plot, ODS Graphics. Enhancing Output – Variable Labels – value labels – SAS Formats. Preventing and correcting errors.

UNIT - III

One-variable descriptive Statistics – Computing one summary measure for a variable – Computing additional Summary Measures. Different types of plots. Two-variable descriptive statistics. Usage of PROC for correlations, Simple Linear Regression and multiple regression analysis.

UNIT - IV

Procedure for one sample and two samples test. Chi-square test. Non parametric tests – Mann-Whitney U Test – Wilcoxon Signed Ranks Test – Kruskal-Wallis Test – Spearman’s Rank Order Correlation.

UNIT - V

Procedure for MANOVA, Hoteling T2, Canonical correlations, Factor analysis and Discriminant analysis.

BOOKS FOR STUDY:1. Geoff Der and Brian S. Everitt.(2009). A Handbook of Statistical Analyses Using SAS. 3rd

Edition. CRC Press, A Chapman & Hall Book.2. Ronald P. Cody and Jeffrey K. Smith. (1987).Applied Statistics and the SAS Programming

Language. 5th Edition. Prentice Hall.3. SAS/STAT User Guide.(2011).SAS Institute Inc., Cary, NC, USA

ELECTIVE - III: DIRECTIONAL DATA ANALYSISUNIT I

Graphical representation of data, ungrouped and grouped data, forms of frequency distribution, descriptive measures, measures of location, mean direction and its properties - median direction, - model direction - circular variance and concentration - circular mean deviation - quantitile deviation- circular mean difference - Correction for mean grouping, trigonometric moments - measures of skewness and kurtosis.

UNIT II Circular models - distribution theory - distribution function – independence – convolution -

Calculus of distribution theory –moments- measures of location and concentration - distributions of an arc, mixtures and multimodal distributions -standard models like lattice

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distributions - uniform distributions - offset normal distribution - wrapped normal - wrapped Cauchy - wrapped Poisson - Circular Normal (Von Mises-Fisher) distributions and their properties including some characterizations - characteristic functions - inversion theorems - Polar distributions - limit theorems - isotropic random walk on the circle - sample distributions for statistics from Von-Mises-Fisher population.

UNIT III Point estimation in parametric models - Cramer Rao type bound – sufficiency - methods of

estimation – MLE - methods of moments and methods of minimum distance.

UNIT IV Testing hypothesis from parametric models mainly from Von-Mises -Fisher population -

Neyman-Pearson and likelihood ratio principles - Tests of significance- Tests for multimodal distributions.

UNIT V Non-parametric methods: Tests for randomness and goodness of fit - Rayleigh's test-

Durand and Greenwood's test- range test - Chi-square type tests - Kuiper's test- Watson’s test - Two sample and multiple sample tests - Uniform score test of Mardia, Watson and Wheeler, Watson's two sample U test - Runs test - Rank sum test - Non-parametric tests for dispersion, multi-sample analogues of the above tests- tests for multimodal data.

BOOKS FOR STUDY:1. Batschelet, E. (1981): Circular Statistics in Biology. Academic press. 2. Jupp, P.E. and Mardia, K.V. (1980): A General Correlation Coefficient for Directional Data

and Related Regression Problems. Biometrika, pp.167-173.3. Khatri, C.G. and Mardia K.(1977): The Von-Mises–Fisher Matrix Distribution in

Orientation Statistics, JRSS,B,Vol.39, pp. 95-106.4. Sarma, Y.R. (1986): Correlation and Regression for Circular Data - A Review. Proceedings

of ISPS.

ELECTIVE - III: CATEGORICAL DATA ANALYSIS UNIT I

Models for Binary Response Variables, Log Linear Models, Fitting Log linear and Logic Models-Building and applying Log Linear Models, Log- Linear- Logit Models for Ordinal Variables.

UNIT II Multinomial Reponse Models - Models for Matched Pairs- Analyzing Repeated Categorical

Response Data - Asymptotic Theory for Parametric Models - Estimation Theory for Parametric Models.

UNIT III Classical treatments of 2 and 3-way contingency tables, measures of association and

nonparametric methods - Generalized linear models - Logistic regression for binary - multinomial and ordinal data - Log-linear models - Poisson regression- Modelling repeated measurements - generalized estimating equations.

UNIT IV Introduction to contingency tables: 2 × 2and r × c tables - tests for independence and

homogeneity of proportions - Fishers exact test - Odds ratio and Logit, other measures of association - Introduction to 3-way tables – full independence and conditional independence - collapsing and Simpsons paradox.

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UNIT V Polytomous logit models for ordinal and nominal response - Log-linear models (and

graphical models) for multi-way tables - Causality, repeated measures, generalized least squares - mixed models, latent-class models, missing data, and algebraic statistics approach.

BOOKS FOR STUDY:1. Agresti, Alan (1996). An Introduction to Categorical Data Analysis, Wiley.2. Bergsma, W., Croon, M.A. and Hagenaars, J.A. (2009). Marginal Models: For Dependent,

Clustered, and Longitudinal Categorical Data. Springer.3. Bishop, Y.M., Fienberg, S.E. and Holland, P.W. (1975). Discrete Multivariate Analysis:

Theory and Practice, MIT Press.4. Edwards, D. (2000). Introduction to Graphical Modeling (Second Edition). Springer.5. Fienberg, S.E. (1980). The Analysis of Cross-Classified Categorical Data. MIT Press.6. Wasserman, L. (2004). All of Statistics: A Concise Course in Statistical Inference. Springer.7. Whittaker, J. (1990). Graphical Models in Applied Multivariate Statistics. Wiley.

ELECTIVE - III: OFFICIAL STATISTICSUNIT I

Introduction to Indian and International statistical systems - Role, function and activities of Central and State statistical organizations - Organization of large scale sample surveys - Role of National Sample Survey Organization - General and special data dissemination systems.

UNIT II Population growth in developed and developing countries - Evaluation of performance of

family welfare programmes - Projections of labour force and manpower - Scope and content of population census of India.

UNIT III System of collection of Agricultural Statistics - Crop forecasting and estimation -

Productivity, fragmentation of holdings - Support prices - Buffer stocks - Impact of irrigation projects.

UNIT IV Statistics related to industries - Foreign trade - Balance of payment - Cost of living –

Inflation - Educational and other social statistics.

UNIT V Indian official statistics : Present official statistical system in India - Methods of collection

of official statistics, their reliability and limitations - Principal publications containing data on the topics such as population, agriculture, industry, trade, prices, labour and employment, transport and communications - Banking and finance - Various official agencies responsible for data collection and their main functions.

BOOKS FOR STUDY:1. Basic Statistics Relating to the Indian Economy (CSO) 1990.2. Family Welfare Yearbook. Annual Publication of D/o Family Welfare.3. Guide to Official Statistics (CSO) 1999.4. Monthly Statistics of Foreign Trade in India, DGCIS, Calcutta and other Govt. Publications.5. Panse, V. G., Estimation of Crop Yields (FAO).6. Principles and accommodation of National Population Censuses, UNESCO.7. Statistical System in India (CSO) 1995.

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ELECTIVE - III: STATISTICAL METHODS FOR BIOINFORMATICSUNIT I

Introduction to Bioinformatics: Definition and History of Bioinformatics - Internet and Bioinformatics - Introduction to Data Mining - Applications of Data Mining to Bioinformatics Problems and Applications of Bioinformatics.

UNIT II Bio computing: Introduction to String Matching Algorithms - Database Search Techniques-

Sequence Comparison and Alignment Techniques - Use of Biochemical Scoring Matrices - Introduction to Graph Matching Algorithms - Automated Genome Comparison and its Implication - Automated Gene Prediction - Automated Identification of Bacterial Operons and Pathways- Introduction to Signaling Pathways and Pathway Regulation - Gene Arrays - Analysis of Gene Arrays.

UNIT III Statistical testing and significance for large biological data analysis- statistical testing –

parametric and non-parametric tests - Resampling based tests - ad hoc tests - Error controlling - multiple testing problems and procedures- Applications.

UNIT IV Overview of bioinformatics - Human genome project - Goals of human genome project -

Bioinformatics and the internet - Useful bioinformatics sites on World Wide Web - Basic principles of computing in bioinformatics: Running computer software - Computer operating system - Software downloading and installation.

UNIT VDatabases: Data life cycle acquisition, modification, use, archiving, repursoning, disposal -

Database technology architecture and management system - Interfaces, software and programming languages - Examples of some bioinformatics database - Use of Databases: Structure databases – visualization of structural data, pattern matching, molecular modeling - Mapping databases – genomic mapping, types of maps - Phylogenetic analysis - an overview – Collaboration.

BOOKS FOR STUDY:1. Bailey, N. T. J. (1995). Statistical Methods in Biology (Third Edition). Cambridge law.2. Baldi, P. and Brunak, S. (1998). Bioinformatics. The MIT Press. 3. Baldi, P. and Brunak, S. Bioinformatics: The Machine Learning Approach. 4. Bergeron, B. (2003). Bioinformatics Computing. Prentice Hall Inc. Eastern Economy

Edition.5. Bhaskarrao, T (2002). Methods of Biostatistics. Paras Publishing.6. Dixit, J. V. (1996). Principles and Practice of Biostatistics (First Edition). M/s Banarasidas

Bharot. 7. Evens, W.J. and Grant, G.R., Statistical Methods in Bioinformatics: An Introduction. 8. Fogel, G.B. and Corne, D.W., Evolutionary Computation in Bioinformatics. 9. Jae K. Lee, (2010). Statistical Bioinformatics. Wiley-Blackwell, New Jersey10. Lesk, A.M. (2002). Introduction to Bioinformatics. Oxford University Press. 11. Letovsky, S.I. (1999). Bioinformatics. Kluwer Academic Publishers. 12. Mont, D.W., Bioinformatics: Sequence and Genome Analysis. 13. Patterson, B.K., Techniques in Quantification and Localization of Gene Expression. 14. Rastogi, S.C., Mendiratta, N. and Rastogi, P. (2004). Bioinformatics: Concepts, Skills &

Applications. CBS Publishers & Distributors, New Delhi. 15. Vyas, S.P. and Kohli, D.V., Methods in Biotechnology and Bioengineering.

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16. Warollaw, A.C. (1925). Practical Statistics for Experimental Biologists. John Wiley & Sons.

ELECTIVE - III: FINANCIAL STATISTICSUNIT I

Introduction – Probability and its distributions – Sampling distributions: t, F, chi-square distributions – Skewness and Kurtosis – Law of large numbers and Central limit theorem – Multivariate normal distributions: Correlation and covariance – Independence and covariance – Linear functions of random variables.

UNIT II Introduction: Net Returns - Gross returns – Log returns – Adjustment for dividends –

Behavior of returns – Random walk models – Origins of the Random walk hypothesis – Efficient Markets Hypothesis (EMH) – Discrete and Continuous Compounding.

UNIT III Time series data - Stationary processes: Weak white noise – Predicting white noise –

Estimating the parameters of a stationary process – Moving Average (MA) processes – ARIMA processes – AIC and SBC - GE daily returns: Choosing the AR order - Three-Month Treasury Bill Rates – Forecasting GE daily log returns and log prices.

UNIT IV Portfolio Theory: Trading Off Expected Return and Risk – One Risky Asset and One-Risk

free Asset – Two Risky assets – Combining two risky assets with risk free asset – Quadratic Programming – Utility Theory.

UNIT V Regime switching models: Introduction – Bull and Bear Markets – Regression on Bull3 –

Other models for Bull/Bear – Bull and Bear portfolios – Copulae and value at risk.

BOOKS FOR STUDY:1. Borowiak, D.S. and Shapiro, A.F. (2013). Financial and Actuarial Statistics: An

Introduction (Second Edition). CRC press.2. Carmona, R. (2012). Statistical Analysis of Financial Data in S-Plus. Springer.3. Rachev, S.T., Hoechstoetter, M., Fabozzi, F.J. and S.M. Focardi. (2010). Probability and

Statistics for Finance. John Wiley & Sons.4. Ruppert, D. (2004). Statistics and Finance: An Introduction. Springer Texts in Statistics5. Sclove, S.L. (2012). A Course on Statistics for Finance. CRC press.

ELECTIVE – IV: TIME SERIES ANALYSIS UNIT I

Models of Time Series – Additive and Multiplicative models – Analysis and forecasting – Elimination of trend – growth curve – Modified experimental curve (Method of three selected points only) - Gompertz curve- Logistic curve with examples.

UNIT IIStationary processes – Auto-covariance and autocorrelation functions and their properties –

partial auto correlation function - Estimation of autocorrelation and its standard error – unit root test.

UNIT III Linear stationary models - stationary and invertability - Autoregressive and Moving average

processes and their autocorrelation functions- Autoregressive moving average processes.30

Linear non-stationary models - Autoregressive integrated moving average processes – integrated moving average processes and Seasonal Autoregressive integrated moving average processes.

UNIT IVBox-Jenkins models: Identification techniques - Initial estimates for different processes –

AR, MA, ARMA - choice between stationary and non stationary models – model diagnostic - model multiplicity - Study of residuals and diagnostic checking - Use of computer packages for the above techniques.

UNIT V Introduction to spectral analysis of weakly stationary processes - periodogram and

correlogram analysis including computations based on Fourier transform. Use of spectral representation to show the existence of autoregressive processes and their

representation as one-sided moving average processes.

BOOKS FOR STUDY:1. Anderson, T. W. (2011): The Statistical Analysis of Time Series. John Wiley & Sons.2. Bloomfield, P. (2004): Fourier analysis of Time Series - An introduction (Second Edition).

John Wiley & Sons.3. Box, G. E. P. and Jenkins, G.M. and Reinsel, G.C. (2013): Time Series Analysis -

Forecasting and Control (Fourth Edition). Holden- Day, San Francisco.4. Brockwell, P. J. and Davis, R. A. (2002): Introduction to Time Series and Forecasting.

Taylor & Francis. 5. Chatfield, C. (1978): The Analysis of Time Series - Theory and Practice (Third Edition).

Chapman and Hall, London.6. Gupta, S. C. and Kapoor, V.K. (2007): Fundamentals of Applied Statistics (Fourth Edition).

Sultan Chand & Sons Company, New Delhi.7. Hannan, E. J. (1960): Time Series Analysis, Methuen, London.8. Kendall, M. G. and Stuart, A. (1976): The advanced theory of Statistics, Vol.3, Charles

Griffin, London.9. Kendall, M. G. (1974): Time Series. Charles Griffin, London.10. Koopmans, L. H. (1995): The spectral analysis of Time Series. Academic press.11. Montgomery, D. C. and Johnson, L. A. (1977): Forecasting and Time Series analysis.

McGraw Hill. 12. Priestley, M. B. (1981): Spectral analysis and Time Series. Griffin, London.

ELECTIVE- IV: STATISTICAL METHODS IN EPIDEMIOLOGYUNIT I

Measures of disease frequency: Mortality/Morbidity rates- incidence rates- prevalence rates - Source of mortality morbidity statistics-hospital records - vital statistics records- Measures of accuracy or validity: sensitivity index - specificity index- Measure of Reliability.

UNIT II Epidemiologic concepts of diseases: Factors which determine the occurrence of diseases -

models of transmission of infection - incubation period - disease spectrum and herd immunity.

UNIT III Observational studies in Epidemiology: Retrospective (case control) & prospective (cohort

or longitudinal) studies - Measures of association: Relative risk, odds ratio, attributable risk- Statistical techniques used in analysis: Cornfield and Garts method - Mantel-Haenszel method-

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Conditional and unconditional matching - Analysis of data from matched samples, logistic regression approach.

UNIT IV Experimental Epidemiology: Clinical & community trials - Statistical Techniques:

Methods for comparison of two treatments - Crossover design with Garts and McNemars test - Randomization in a clinical trial - sequential methods in clinical trials - clinical life tables - assessment of survivability in clinical trials.

UNIT V Mathematical Modeling in Epidemiology:(deterministic & stochastic) simple epidemic

model - generalized epidemic model- Reed-Frost and Green-wood models - models for carrier borne and host vector diseases - Estimation of latent and infectious periods - geographical spread of the disease - simulation of an epidemic.

BOOKS FOR STUDY:1. Armitage. (1980): Sequential medical trials, Charles C. Thomas2. Bailey, N.T.J. (1987): The Biomathematics of Malaria. Oxford University Press,

Incorporated.3. Fleiss, J.L. (1981): Statistical Methods for Rates and Proportions. John Wiley & Sons,

Incorporated, New York.4. Franeuthal. (1980): Mathematical Modernization in Epidemiology, Springer Verlag.5. Gross and Clark. (1989): Survival Distributions- Reliability Application in Biomedical

Sciences, University Microfilms.6. Kahn, H.A. and C.T. Sempos. (2007): Statistical Methods in Epidemiology (Second

Edition). Oxford University press, N.Y.7. Kahn, H.A. (1983): An introduction to Epidemiologic methods. Oxford University press,

N.Y. (Digitized 2007). 8. Lilienfeld and Lilenfeld. (1994): Foundations of Epidemiology (Third edition). Oxford

Univ. Press.9. Macmahon, B. and Pugh, T.E. (1970): Epidemiology-Principles and methods, Little, Brown

and Co. Boston/Massachusetts.10. Pocock, S.J. (2004): Clinical Trials - A Practical Approach, John Wiley.11. Fletcher, R. and Fletcher, S.W. (2013). Clinical Epidemiology: The essentials. Lippincott

Williams & Wilkins.12. Rothman, K.J. (1986): Modern Epidemiology. Lippincott Williams & Wilkins.13. Sackett, D.L (1991): Clinical Epidemiology- A Basic Science for Clinical Medicine. Little

Brown.

ELECTIVE – IV: BAYESIAN METHODSUNIT I

Statistical decision theory – loss functions – 0-1, absolute error, squared error and LINEX loss functions – risk function – minimax solution – prior distribution – Bayes risk – Bayes solution to decision problems.

UNIT IISubjective probability – its interpretation and evaluation - Subjective determination of prior

distributions - Improper prior, non informative prior, invariant prior, Jeffreys non informative prior and natural conjugate prior – family of distributions admitting natural conjugate prior.

UNIT III

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Point estimation – Bayes estimators under various loss functions – generalization to convex loss functions - Evaluation of the estimate in terms of posterior risk – comparison with frequentist methods.

UNIT IVInterval estimation – credible interval, highest posterior density region - Comparison of

interpretation of the confidence co-efficient of an interval by Bayesian and frequentist methods – simple problems.

UNIT VBayesian testing of statistical hypotheses – specification of the appropriate form of the prior

distribution for Bayesian hypothesis testing problem – prior odds, posterior odds, Bayes factor and their computations to various hypotheses testing problems – specification of Bayes tests.

BOOKS FOR STUDY:1. Bansal, A.K. (2007): Bayesian Parametric Inference. Narosa Publishing House, New Delhi.2. Berger, J.O. (1985): Statistical Decision Theory and Bayesian Analysis (Second Edition).

Springer Verlag, New York.3. Bernardo, J.M. and Smith, A.F.M. (2000): Bayesian Theory. John Wiley & Sons,

New York. (Reprint 2009).4. Gelman, A., Carlin, J.B., Stern, H.B. and Rubin, D.B. (2013): Bayesian Data Analysis

(Third Edition). CRC press.5. Ghosh, J.K., Delampady, M. and Samanta, T. (2010): An Introduction to Bayesian

Analysis: Theory and Methods. Springer Verlag, New York. 6. Lee, P.M. (2012): Bayesian Statistics – An Introduction (Fourth Edition). John Wiley &

Sons, London.7. Leonard, T. and J.S.J. Hsu. (1999): Bayesian Methods: An Analysis for Statisticians and

Interdisciplinary Researchers. Cambridge University Press, London.8. Robert, C.P. (1994): The Bayesian Choice: A Decision-Theoretic Motivation (Second

Edition). Springer Verlag, New York.9. Robert, C.P. and Casella, G. (2004): Monte Carlo Statistical Methods (Second Edition).

Springer Verlag, New York. (Reprint 2010)

ELECTIVE - IV: DATA STRUCTURESUNIT I

Mathematics Review - Background model – Algorithm analysis – running time calculations – General rules – Solutions for the maximum subsequence sum problem – Logarithms in the running time – checking analysis.

UNIT IIAbstract Data Type (ADT) – List ADT – Array implementation of lists – Linked List –

Doubly and circularly linked lists – Stack ADT – Queue ADT – Trees: Binary trees – Binary search trees.

UNIT IIIHashing: Hash function – open Hashing – Closed Hashing – Priority Queues (Heaps):

Binary Heap – Applications of priority queues Sorting: Insertion Sort – Shell Sort – Heapsort – Mergesort – Quickesort.

UNIT IVGraph Algorithms: Topological sort – Shortest Path algorithms – Network Flow Problems –

Minimum Spanning tree – Application of DFS.33

UNIT VAlgorithm Design Techniques – Geedy Algorithms: Scheduling problem – Huffman codes

– Approximate bin packing – Divide and Conquer: Running time of Divide and Conquer algorithms – Closest – Points problem – The selection problem – Theoretical Improvements for Arithmetic Problems.

BOOKS FOR STUDY:1. Gilberg, R.F. and B. A. Forouzan. (2004): Data structures: A Pseudocode Approach with

C++, Cengage Learning.2. Kanetkar, Y. (2003): Data Structures Through C, BPB Publications, New Delhi.3. Kruse, R.L. (1994): Data Structures and Program Design (Third Edition), Prentice – Hall,

Inc.4. Lipschutz, S. and G. A. Vijayalakshmi pai. (2006): Data Structures, Tata McGraw Hill

Education Private Limited, New Delhi.5. Sahni, S. (2005): Data Structures, Algorithms and Applications in C++ (Second Edition).

Silicon Press.6. Vijayalakshmi Pai, G. A. (2008): Data Structures and Algorithms, Concepts, Techniques

and Applications. Tata McGraw – Hill Publishing Company Limited, New Delhi.7. Weiss, M. A. (2013): Data Structures and Algorithms Analysis in C++ (Fourth Edition).

Pearson Education.

ELECTIVE - IV: STATISTICAL DECISION THEORYUNIT – I

Decision problem – 2- person game – Utility theory – Loss Functions – Expected Loss – Decision Rules (non-randomized and randomized) – Decision principles.

UNIT – IIConcept of admissibility and completeness – Bayes rules – Admissibility of Bayes rules.

UNIT – IIISupporting and separating hyper-plane theorems – Minimax theorem of finite parameter

space – Minimax estimators of Normal and Poisson means – Admissibility of minimax rules.

UNIT – IV Invariant decision rules – Location parameter problems – Invariance and minimaxity –

Admissibility of invariant rules – Complete class theorem- Complete and essentially complete classes in simple estimation and testing situations.

UNIT – VSufficient statistics essentially complete classes of rules based on sufficient statistics –

Complete sufficient statistics.

BOOKS FOR STUDY:1. Berger, J.O. (1985): Statistical Decision Theory and Bayesian Analysis (Second Edition). 2. Bernando, J.M. and A.F.M. Smith (2009): Bayesian Theory, John Wiley & Sons.3. Pratt, J.W., H. Raiffa and R. Schlaifer. (1995). Introduction to Statistical Decision Theory,

MIT Press.4. Rao, C.R. (2009): Linear Statistical Inference and its Applications (Second Edition), John

Wiley & Sons34

5. Robert, C.P. (1994): The Bayesian Choice: A Decision Theoretic Motivation, Springer. (Reprint 2010).

6. Rohatgi, V.K. (1988): An Introduction to Probability and Mathematical Statistics. Wiley Eastern, New Delhi.

ELECTIVE - IV: GAME THEORY AND ITS APPLICATIONSUNIT – I

Introduction - The Formulation of Two-Person, Zero-Sum Games- Solving simple Games- A Prototype Example – Games with Mixed Strategies – Graphical Solution Procedure – Solving by Linear Programming.

UNIT – IICombination games –Definition of Combinatorial game – The fundamental theorem for

combinatorial games – Nim–Hex and other games – Tree games – Grundy functions – Bogus Nim–Sums.

UNIT – IIITwo Person Zero – Sum games – Games in normal form – Saddle points and equilibrium

pairs Max-min and Minimax – Mixed Strategies – 2 x 2 matrix games – 2 x n, m x 2, and 3 x 3 matrix games – Linear Programming.

UNIT – IV The Simplex Method the fundamental theorem of duality solution of two person – Slack

variables perfect canonical linear programming problem – the Simple method – Pivoting – The perfect phase of the simplex method –The Big M method – Bland’s rules to present cycling – Duality and the Simple method – Solution of game metrics.

UNIT – VGames in coalitional form – The imputation of set and the core – Linear production games –

Dominance – D-core – Stable sets – Shapley value – Nucleolus – Bargaining games.

BOOKS FOR STUDY:1. Binmore, K. (1992). Fun and Games: A Text on Game Theory, Heath, Lexington, MA.2. Chatterjee, K., and W. F. Samuelson. (2001). Game Theory and Business Applications,

Kluwer Academic Publishers, Boston.3. Forgo, F., Szep, J. and F. Szidarovsky. (1999). Introduction to the Theory of Games

Concepts, Methods, Application, Kluwer Academic Publishers, Boston.4. Hillier, F.S. and G. J. Lieberman. (2008). Introduction to Operations Research Concepts and

Cases. (Eighth Edition). Tata McGraw-Hill Publishing Company Limited, New Delhi 5. Mendelson, E. (2004). Introducing Game Theory and its Applications. CRC Press.

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SYLLABUS FOR SUPPORTIVE PAPERS

1. DESCRIPTIVE STATISTICSUNIT I

Origin - Scope – Functions, limitations, uses and misuses of statistics - Classification and Tabulation of data - Diagrammatic and Graphical representation of data.

UNIT IIMeasure of Central tendency - Measures of Dispersion - Relative measures of dispersion -

skewness and kurtosis - Lorenz curve.

UNIT IIIElementary probability space - Sample space - discrete probability, independent events -

Mathematical and Statistical probability -Axiomatic approach to probability - Addition and multiplication theorems - conditional probability – Bayes’ theorem - Simple problems. UNIT IV

Random variables - Discrete and continuous random variables - Distribution function – probability mass function and probability density function of a random variable - Expectation of a random variable - evaluation of standard measures of location, dispersion, skewness and kurtosis.

UNIT VSimple linear correlation and regression - Scatter diagram - Karl Pearson’s correlation

co-efficient and its properties - Spearman’s correlation co-efficient. Regression equations– fitting of regression equations - regression coefficients and its properties.

BOOKS FOR STUDY:1. Goon, A.M., Gupta, M.K. and Dasgupta, B. (2008): Fundamentals of Statistics,

Volume-I, World Press Ltd, Calcutta. 2. Gupta, S.C. and V.K. Kapoor. (2000): Fundamentals of Mathematical Statistics,

Sultan Chand and Sons, New Delhi.3. Hogg, R.V., McKean, J.W. and Craig, A.T. (2013). Introduction to Mathematical

Statistics (Seventh Edition). Pearson Education Ltd.4. Spiegel, M.R., Schiller, J. and Srinivasan, R.A. (2012): Probability and Statistics,

Schaum's Outline Series (Fourth Edition). McGraw- Hill Publishing Company, New Delhi.

2. STATISTICS FOR BEHAVIOURAL SCIENCESUNIT I

Nature and scope of statistics - characteristics and limitation of statistics - statistical investigation - preparation of questionnaire - design of sampling - simple random, stratified and systematic sampling - collection of data - primary and secondary data.

UNIT IIProcessing and presentation of data - Classification of data - tabulation of data - Formation

of frequency tables - Diagrammatic presentation of statistical data - bar diagrams - pie diagrams and pictograms - simple problems - Graphical presentation of statistical data - Histogram, frequency curves and Ogive curve - simple problems.

UNIT III36

Measures of central tendency - mean, median, mode - simple problems - measures of dispersion - range, mean deviation, quartile deviation and standard deviation - relative measures of dispersion - simple problems.

UNIT IVConcept of Skewness and Kurtosis - Karl Pearson’s and Bowley's coefficients of Skewness-

moments- coefficients of Skewness and Kurtosis - simple problems.

UNIT VCorrelation: Scatter diagram - simple correlation, Rank correlation. Regression - simple

regression lines (without proof) - Tetrochoric correlation, Phi coefficient and Kendall’s co-efficient - simple problems.

BOOKS FOR STUDY:1. Camphell, R.C. (1989): Statistics for Biologists, Cambridge University Press, London.2. Garret, H.E. and R.S. Woodworth. (2006): Statistics in Psychology and Education. Cosmo

Publications, New Delhi.3. Goon, A.M., Gupta, M.K. and Dasgupta, B. (2008): Fundamentals of Statistics, Volume-I,

World Press Ltd, Calcutta. 4. Gupta, S.C. and V.K. Kapoor. (2000): Fundamentals of Mathematical Statistics (Tenth

Edition). Sultan Chand and Sons, New Delhi.5. Saxena, H.C. (1967): Elementary Statistics, Sultan Chand & Co., New Delhi.6. Tate, M.W. (1964): Statistics in Education. Macmillan Co., New York.

3. COMPUTER ORIENTED STATISTICAL METHODSUNIT I

Introduction to Computing - Computer Codes and Arithmetic Overview of BASIC - Sampling and Frequency Distribution : Sampling - Frequency Distribution - Measures of Central Tendency - Measures of Dispersion - Moments - Computation of Moments.,

UNIT IIDiscrete Probability Distributions: Probability - Characteristics of Probability - Discrete

Distributions - Binomial Distribution - Poisson Distribution - Hypergeometric Distribution – Properties and Numerical problems.

UNIT IIICurve Fitting: Linear Regression - Least Squares Fit - Nonlinear Fit - Fitting a Polynomial

Function.

UNIT IVCorrelation : Coefficient of Correlation - Properties of Correlation Coefficient - Rank

Correlation - Multiple Correlation - Partial Correlation.

UNIT VTests of Significance: Small sample and large sample tests - t-Test - F-Test and χ2 test.

BOOKS FOR STUDY: 1. Balagurusamy, E. (2000): Computer Oriented Statistical and Numerical Methods,

Macmillan Publishers India Limited.2. Enslein, K., Ralston, A. and Wilf, H.S. (1976): Statistical Methods for Digital Computers.

John Wiley & Sons, New York.

4. PROBABILITY AND STATISTICS

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UNIT I Basic ideas of Probability - Axiomatic approach to probability - Elementary probability

spaces – Addition and multiplication theorems of probability – conditional probability - Independent events – Bayes’ Theorem.

UNIT IIRandom Variables - Distribution function probability mass function and probability density

function - Mathematical expectation - Discrete distributions - Binomial, Poisson and Negative Binomial distributions.

UNIT IIIContinuous distributions - Uniform, Normal, Exponential, Gamma and Beta distributions -

Student-t, Chi-square and F distributions.

UNIT IVCorrelation and Regression - Partial and Multiple Correlation - Tests of Significance -

Tests based for population mean and variance - Testing for two means, variances - Contingency table - Chi-square goodness of fit tests.

UNIT VSampling - Census and Sampling method - Sampling and non sampling errors - Simple

random sampling - Sampling from finite populations with and without replacements - Estimates of mean - Design of experiments: The Principle of Randomization, Replications, Local control - Analysis of variance - One-way and Two-way classifications - Completely Randomized Design - Randomized Block Design and Latin Square Design.

BOOKS FOR STUDY:1. Gupta, S.C and Kapoor, V.K. (2000): Fundamental of Mathematical Statistics (10 th Edition),

Sultan Chand and Sons, New Delhi.2. Ross, S.M. (2014). Introduction to Probability Models. Academic press.3. Spiegel, M.R., Schiller, J. and Srinivasan, R.A. (2012): Probability and Statistics, Schaum's

Outline Series (Fourth Edition). McGraw- Hill Publishing Company.4. Walpole, R.E., Myers, R.H., Myers, S.L and Ye, K.E. (2011): Probability and Statistics for

Engineering and Scientist (Ninth Edition). Pearson Education.

5. STATISTICAL METHODSUNIT I

Definition of Statistics and its applications in various disciplines - Collection of Data - classification, Tabulation and Graphical representation of data - construction of univariate and Bivariate frequency distribution - Measures of central tendency - Measures of dispersion - coefficient of variation.

UNIT IIRandom experiment - sample space - events - mathematical and statistical definition of

probability - conditional probability – Bayes’ theorem - Random variables - Distribution functions - moments - Binomial distribution - Poisson distribution - Normal distribution and their properties.

UNIT IIIScatter diagram - Karl Pearson's coefficient of correlation - concurrent deviation method -

coefficient of determination - Spearman's Rank correlation - Linear regression – fitting of regression lines.

UNIT IV

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Tests of significance - hypotheses - two types of errors - power function - critical region - level of significance - small sample tests based on t and F distributions. Chi-square test of goodness of fit - contingency table - Test of independence of factors - Large sample tests.

UNIT VTest of equality of several population means one way and two way analysis of variance -

Non-parametric tests Sign, Run and Median tests - two sample rank test. Sampling and its uses, sampling methods - Simple random sampling, systematic and stratified.

BOOKS FOR STUDY:1. Agarwal, B.L. (2013): Basic statistics. Anshan Publications 2. Sharma, J.K. (2007): Business Statistics (Second Edition). Pearson Education, New Delhi.3. Sokal, P.R. and Rohlf, F.J. (1969): Bio Statistics. W.H. Freeman and Co., San Francisco.

6. BIO-STATISTICSUNIT I

Measures of Central tendency: Arithmetic Mean, Median, Mode. Measures of Dispersion: Range, Inter-Quartile Range, Standard Deviation and Coefficient of Variation.

UNIT II Basic concepts of Probability - Set theoretic definition of probability - Addition and

Multiplication Theorems of probability (statements only) - Binomial distribution - Poisson distribution - Normal distribution - their properties and importance in biology.

UNIT III Simple Correlation- Regression – Bi-serial correlation coefficient - Kendall’s coefficient of

correlation - Tetrochoric correlation coefficient - Partial and Multiple correlation coefficients (Three variables). Simple problems with application in biology.

UNIT IVSmall sample and Large sample tests: Test for the significance of population mean when

population variance is (i) known and (ii) unknown - Tests of significance for testing the equality of means of two normal populations when population variances (i) known and (ii) unknown - Chi-square test - test for independence of the attributes - test for goodness of fit - Coefficient of contingency.

UNIT VAnalysis of Variance: One way classification - Two way classification - Kruskal-Wallis

one way analysis of variance by ranks, Friedman two-way analysis of variance by ranks.

BOOKS FOR STUDY:1. Campbell, R.C. (1989): Statistics for Biologists. Cambridge University Press, London.2. Daniel, W.W. (2008): Bio-Statistics: A Foundation for Analysis in the Health Science. John

Wiley & Sons, Incorporated.3. Glantz, S.A. (2012): Primer of Bio-Statistics (Seventh Edition). McGraw-Hill Professional

Publishing, USA.4. Sokal, R.R. and Rohlf, F.J. (1969). Biometry: The Principles and Practice of Statistics in

Biological Research (Third Edition). San Francisco, California, Freeman and Company.

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7. MATHEMATICAL ECONOMICS

UNIT IElasticity of Demand - Total, Average and Marginal Cost Curves - Relation between

Average and marginal Cost Curves - Minimum Average cost-Cost function in Cubic Form - Total Average - Marginal Revenue Curves - Total Revenue - Conditions for Profit Maximization - Effects of Taxation and Subsidy on monopoly.

UNIT IIIndifference Curve - Rate of Commodity substitution (RCS)-Maximization of Utility -

Income and substitution Effects – Important Results from Slutsky Equation - Elasticity form of Slutsky Equation.

UNIT IIIProduction Function - Constant Product Curves: Isoquants - Shape of Isoquants and Ridge

Lines-Least Cost Combination (constrained Cost Maximisation) - Constrained Profit Maximization - Homogeneous Function: Definition and Properties- Properties of Linearly Homogeneous Functions -Cobb-Douglas production function - Expansion Path for Cobb-Douglas Function - Elasticity of substitution- Elasticity of substitution of Linearly Homogeneous Function - C.E.S. Function.

UNIT IVMultiple Production by Monopolist - Discriminating monopoly - Duopoly - Consumer's

Surplus - Producer's Surplus.UNIT V

Input-Output Analysis: Assumptions - Closed and open Input-Output model - coefficient Matrix and Open model - The Hawkins-Simon condition (The Viability of the system ) - solution for Industries - An Alternative Way for the Inverting the Leontief Matrix - Interpretation of the Alternative Formulation - Coefficient Matrix and closed model - Consumption function - Dynamic Input-Output model - Possible Weaknesses and Limitations of Input-Output Analysis.

BOOKS FOR STUDY:1. Allen .R.G.D. (2008): Mathematics for Economists, ELBS series, London.2. Daus, P.H. and Whyburn, W.M. (1962): Mathematics for Economists, Addison and

Wesley, Amsterdam.3. Draper, J. and Klingman, J. (1972): Mathematical Analysis: Business and Economic

Applications, Harper – Row publishing company.4. Henderson, J.M. and Quandt, R.E. (1967): Micro Economic theory, McGraw- Hill. 5. Mehta, B C. and Madnani, G.M.K. (1977): Mathematics for Economists (Third Edition),

Sultan Chand, New Delhi.6. Tintner .G. (1966): Mathematics and Statistics for Economists. Holt, Rinehart and Winston.

8. ADVANCED STATISTICAL METHODSUNIT I

Basic operations of matrix - Determinant and inverse of matrices - Idempotent matrix - solutions of simultaneous equations - Univariate normal distribution and its extension to multivariate normal (non-singular case only) distribution and its properties - estimates of parameters - inference about populations mean vector.

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UNIT IIMultiple correlation - relationship with simple correlations - tests of significance of

multiple correlation - multiple regression - interpretation of SPSS outputs regarding fitting of multiple linear regression model and computation of multiple correlation co-efficient.

UNIT IIIClassifications of two populations - General classification problem - Fisher's discriminant

function - Principal components - properties - finding first principal component - iterative methods.

UNIT IVFactor analysis - Orthogonal factor model - factor rotation and inference - Clustering -

similarity measure - Hierarchical clustering methods, Canonical variable and canonical correlation.

UNIT VPrinciples of experiments - CRD, RBD and LSD - Basic ideas of factorial experiments -

concept of hierarchical model - Non-parametric methods – chi-square test - sign test - Wilcoxon test - Run test - Mann - Whitney test.

Note:No derivation of the results required. Importance will be given only to application and

understanding of the concepts.

BOOKS FOR STUDY:1. Cochran, W.G. and Cox, G.M. (1975): Experimental designs, John Wiley & Sons.2. Dunteman, G.H. (1984): Introduction to Multivariate Analysis, Sage Publications, New

Delhi.3. Rencher, A.C. (2003): Methods of Multivariate Analysis (Second Edition), John Wiley &

Sons.*****

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