In a sequence of independent identical trials with two possible outcomes on each trial, S and F, and with P(S) = p, what is the probability that exactly y trials will occur before the rth success? Define a random variable X = y trials before the before the first success, y = r - 1, r, r+ 1,.... Then, X = Y-1, where Y has the negative binomial distribution with parameters r and p. Thus, p(x) = ,y=r-1, r, r+ 1,....

In a sequence of independent identical trials with two possible outcomes on each trial, S and F, and with P(S) = p, what is the probability that exactly y trials will occur before the rth success? Define a random variable X = y trials before the before the first success, y = r - 1, r, r+ 1,.... Then, X = Y-1, where Y has the negative binomial distribution with parameters r and p. Thus, p(x) = ,y=r-1, r, r+ 1,....

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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