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1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent increments Ie. Stochastic process with stationary increments 2. Discrete LV.' s and Generating functions: 2a. Binomial LV. 2b. Poisson LV. 2c. Geometric LV. 2d. Negative Binomial LV. Homework: Kao, Edward (1997). An introduction to stochastic processes. Ch. 1, Sec. 1,2 (till the Law of total probability). Problems: 1# 2, 3

Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

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Page 1: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

1. Introductionla. Definition of a stochastic processlb. Stochastic process with independent incrementsIe. Stochastic process with stationary increments

2. Discrete LV.' s and Generating functions:2a. Binomial LV.

2b. Poisson LV.

2c. Geometric LV.

2d. Negative Binomial LV.

Homework: Kao, Edward (1997). An introduction to stochastic processes.Ch. 1, Sec. 1,2 (till the Law of total probability).

Problems: 1# 2, 3

Page 2: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

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-------:-\->--k-k- Q'7 ~''t.er1 t , 't4c: --f2- -?> R

x+-:*-

Page 3: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

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_____ ~'J

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Page 4: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

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Page 5: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

....---- Lt, ~.fncJ.O-sf.z'c hCRJ1 /J.c//-t t'h~

- l'vtcf.e~s. •

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Page 6: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

_______ "_E_~a_y.4ff!!.: LeA- ~ =: & /W.~ ~ &cc,'v"'-6,

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- (j= Il

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___ ~lE--(~~--Kj= ~+ I k Q'Y k~o,t2,."/< .•.

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Page 7: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

----:::::;:::::-2.. "-XI'S Ct.)., •...V '1 ~ SON.~ Ju w..h'Dkl S

U:. '~~ =- tz.-) "'- Cl.." ) b - D I I, 2)

P~""- H.~R.V1R ~ &u4~...i fk ~____ (....1_--'-c..-..z;;.j)...fi'.L-.L-~ ~ ~. v, X 0/)

~ ~> ~ CA___ o....-'-'-(:C-...J---/::'_!; l',;) :< ;< a '1 r- =0 E \!d---I---~-

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ert ~ (~) ~X fV ~ =1P(X=h) ~/ (?{d

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______ en ::::'Z {)J1-1,tl1-YJ1flIl ==0

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Page 8: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

_ h-Vl1:c

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Page 9: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

,

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.- £- 2== Q =6 -:c- "'- 2= GL_· 2- -'\tl-I.L- .tr(

It\. c \L. \'Yl =:::0

-------------------------_ .._--~-?-~-_._------------------_._---_ ..._ ...._..-_._._.._----

Page 10: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

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.-5(-

Page 11: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

2 Q BZMnu.'u£ r, v,-- . -----

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---------- ,______ VL. J4-., d h- i h--

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Page 12: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

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------0-)- . -~.(~~~"='-,)---------.--.----.-~-L+) -=- 1-€------------------

, E-\51 = r~ =- A6 (2)) cz ~+~I~ 0 (2)( \ '\'L"I K (£-) = 'd f'. rX () = c'

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Page 13: Homework: Kao, Edward (1997). An introduction to ...rmnatsak/Note1_763_spr09.pdf · 1. Introduction la. Definition of a stochastic process lb. Stochastic process with independent

0.",= tP (X'=h) "::::t" ~ ) 'n~O, I, '2.) ., .

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