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Consider independent trials, each of which results in outcome i, i = 0, 1, .,k, with probability Pi, where Eo Pi =1. Let N denote the number of trials needed to obtain an outcome that is not equal to 0, and let X be that outcome. (a) Find P(N = n), n 21 (b) Find P(X = j), j = 1,., k c) show that P(N=n, X=j) = P(N=n)P(X=j)

Consider independent trials, each of which results in outcome i, i = 0, 1, .,k, with probability Pi, where Eo Pi =1. Let N denote the number of trials needed to obtain an outcome that is not equal to 0, and let X be that outcome. (a) Find P(N = n), n 21 (b) Find P(X = j), j = 1,., k c) show that P(N=n, X=j) = P(N=n)P(X=j)

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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Consider independent trials, each of which results in outcome i, i = 0, 1,., k, with probability Pi, where Eo Pi =1. Let N denote the number of trials needed to obtain an outcome that is not equal to 0, and let X be that outcome. (a) Find P(N = n), n 2 1 (b) Find P(X = j), j = 1, ., k c) show that P(N=n, X=j) = P(N=n)P(X=j)
Transcribed Image Text:Consider independent trials, each of which results in outcome i, i = 0, 1,., k, with probability Pi, where Eo Pi =1. Let N denote the number of trials needed to obtain an outcome that is not equal to 0, and let X be that outcome. (a) Find P(N = n), n 2 1 (b) Find P(X = j), j = 1, ., k c) show that P(N=n, X=j) = P(N=n)P(X=j)
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