PROBABILITY AND STATISTICS

BS-338

Probability and Statistics

Catalogue No: BS-338

Credit Hours: 3

Text Book: Advanced Engineering

Mathematics by E.Kreyszig

Reference Books

Probability and Statistics by Murray R. Speigel

Probability and Statistics for Engineers and

Scientists by Walpole

Course Objectives

To teach students basics of

Probability and Statistics with

applications related to

different disciplines of

engineering.

Course Outcomes

Present sample data and extract its important features

Understand different discrete and continuous probability distributions

Estimate different population parameters on the basis of samples

Implement quality control measures

Course Outline

Graphical Representation of Data: Stem-

and-Leaf Plot, Histogram, and Boxplot

Mean, Standard Deviation, Variance

Sample Space, Experiment Outcomes,

Sampling, and Set theory

Introduction to theory of Probability, and

Conditional Probability

Permutations and Combinations

Course Outline Random Variables and Probability

Distributions Mean and Variance of a Distribution,

Expectation, Moments Binomial, Poisson, Hypergeometric

and Normal distributions Distributions of several Random

Variables Random Sampling Point Estimation of Parameters

Course Outline

Confidence Intervals

Testing of Hypothesis and Decisions

Quality Control and Control Charts

Acceptance Sampling, Errors and

Rectification

Goodness of Fit and Chi-square Test

Regression Analysis

Probability

A probability provides a quantatative description of the likely occurrence of a particular event.

StatisticsStatistics is a discipline that allows researchers to evaluate conclusions derived from sample data. In practice, statistics refers to a scientific approach used to: Collect Data Interpret and Analyze Data Assess the Reliability of Conclusions based

on Sample Data

Descriptive Statistics

Collection, Organization, Summarization and Presentation of Data

Inferential Statistics Makes inferences from Samples

to Population

Generalization from Samples to Population, Performing Estimates and Hypothesis Tests, Determining relationship among Variables, and making Predictions

Variable

A variable is an attribute that

describes a person, place, thing,

or idea

The value of the variable can

"vary" from one entity to another

Qualitative vs Quantitative Variables

Qualitative variables take on values that are names or labels. The colour of a ball (e.g., red, green, blue)

Quantitative variables are numeric. They represent a measurable quantity. For example, population of a city

Discrete vs Continuous Variables

Quantitative variables can be further

classified as discrete or continuous.

If a variable can take on any value

between its minimum value and its

maximum value, it is called a

continuous variable; otherwise, it is

called a discrete variable.

Univariate vs Bivariate Data

Univariate Data. A study that looks at only one variable, is said that we are working with univariate data.

Bivariate Data. A study that examines the relationship between two variables, is said working with bivariate data.

ProblemWhich of the following statements are true? I. All variables can be classified as

quantitative or categorical variables. II. Categorical variables can be continuous variables. III. Quantitative variables can be discrete variables.

(A) I only (B) II only (C) III only (D) I and II (E) I and III

Problem The following measurements were

recorded for the drying time, in hours, of a certain brand of latex paint:3.4 2.5 4.8 2.9 3.62.8 3.3 5.6 3.7 2.84.4 4.8 5.2 5.0 4.8

What is the sample size for the above sample?

Calculate the Sample Mean for this data. Calculate the Sample Median Compute the 20% trimmed mean for the

above Data Set.

Categorical Frequency Distribution

Twenty Five soldiers were given a blood test to determine their blood type. The data set is:A B B AB OO O B AB BB B O A AA O O O ABAB A O B A

Grouped Frequency Distribution

Carbon Content [%] of coal

89 90 89 84 8088 90 89 88 9085 87 86 82 8576 89 87 86 86

Find the Range of above Data Set. Formulate Frequency Distribution Table. Represent the Data by a Histogram.

Problem Find the Variance and Standard Deviation for

the Data Set: 10 60 50 30 40 20

Steps to calculate Variance and Standard Deviation Find the Mean Subtract the Mean from each Data Value Square each result Find sum of squares Divide sum by N to get the Variance (291.7) Take Square Root, to find Standard Deviation

(17.1)

Problem

Draw a Stem-and-Leaf Plot and Box-

and-Whisker Plot for the following

set of values:12, 13, 21, 27, 33, 34, 35, 37, 40, 40, 41

Problem Set 24.1Question 7

Represent the data by a Stem-and-Leaf Plot, a Histogram and a Boxplot:

Reaction Time [sec] of an automatic switch: 2.3 2.2 2.4 2.5 2.3 2.3 2.4 2.1

2.52.4 2.6 2.3 2.5 2.1 2.4 2.2 2.3 2.5 2.4 2.4

Problem

Find the Mean and Compare it with Median.

Find the Standard Deviation and Compare it with the Interquartile Range:

2.3 2.2 2.4 2.5 2.3 2.3 2.4 2.1 2.52.4 2.6 2.3 2.5 2.1 2.4 2.2

2.3 2.5 2.4 2.4

Problem

Complete a stem-and-leaf plot for the following list of values:

100,  110,  120,  130,  130,  150,  160,  170,  170, 190, 110,  230,  240,  260,  270,  270,  280.  290,  290

QUIZ # 1DE-32(B) – 17 SEP 2012

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint:3.4 2.5 4.8 2.9 3.62.8 3.3 5.6 3.7 2.84.4 4.8 5.2 5.0 4.8

Represent the data by a Stem-and-Leaf Plot, and a Boxplot. (Marks: 2 +3)

QUIZ # 1DE-32(A) – 18 SEP 2012

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint:3.4 2.5 4.8 2.9 3.62.8 3.3 5.6 3.7 2.84.4 4.8 5.2 5.0 4.8

Make a Frequency Distribution Table and represent the data by a Boxplot. (Rows 1, 3, 5)

Find the Standard Deviation and Compare it with the Interquartile Range. Also graph its Stem-and-Leaf plot. (Rows 2, 4, 6)

(Marks: 2 +3)