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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)

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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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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