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Define a Bernoulli process by the series of independent and identically dis- tributed random variables {X;} with i = 1..00 such that: P(X; 1) = p P(X; 0) = 1– p The event X; a) Let {Nn} be the number of successes by time n. What is P(Nn = k)? b) Let T be the time of the kth success. Show that: = 1 denotes a "success" at time i. %3D P(Tk+1 - Tk = n|To, ...,Tk) = p(1 – p)"-1 ..... c) Calculate the moment generating function: E[e*T\]

Define a Bernoulli process by the series of independent and identically dis- tributed random variables {X;} with i = 1..00 such that: P(X; 1) = p P(X; 0) = 1– p The event X; a) Let {Nn} be the number of successes by time n. What is P(Nn = k)? b) Let T be the time of the kth success. Show that: = 1 denotes a "success" at time i. %3D P(Tk+1 - Tk = n|To, ...,Tk) = p(1 – p)"-1 ..... c) Calculate the moment generating function: E[e*T\]

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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please help with all 3 subparts of the bernoulli process 

Define a Bernoulli process by the series of independent and identically dis- tributed random variables {X;} with i = 1..0 such that: P(X; 1) = p P(X; 0) — 1 — р The event X; = 1 denotes a "success" at time i. a) Let {Nn} be the number of successes by time n. What is P(N, = k)? b) Let T be the time of the kth success. Show that: P(Tr+1 Tk = n|To, ...,T;) = p(1 – p)"-1 пТо, c) Calculate the moment generating function: E[e*T*]
Transcribed Image Text:Define a Bernoulli process by the series of independent and identically dis- tributed random variables {X;} with i = 1..0 such that: P(X; 1) = p P(X; 0) — 1 — р The event X; = 1 denotes a "success" at time i. a) Let {Nn} be the number of successes by time n. What is P(N, = k)? b) Let T be the time of the kth success. Show that: P(Tr+1 Tk = n|To, ...,T;) = p(1 – p)"-1 пТо, c) Calculate the moment generating function: E[e*T*]
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