PMF: The possible values of a Negative Binomial random variable are x = r,r + 1,... and the probability that the rth success occurs on the xth trial is File Preview nb(x;r,p) = FACT: If X1,..., X, are independent Geometric(p) random variables, then r X = Σ Xi Σ X; ~ Negative Binomial (r,p) i=1 PROPOSITION: The expected value and variance of a Negative Binomial random variable with parameters r and p are E(X) = r 1 - p V(X) =r " Ρ p² Example: You roll a fair six-sided die until you see the third six. What is the probability that this happens on the tenth roll?

PMF: The possible values of a Negative Binomial random variable are x = r,r + 1,... and the probability that the rth success occurs on the xth trial is File Preview nb(x;r,p) = FACT: If X1,..., X, are independent Geometric(p) random variables, then r X = Σ Xi Σ X; ~ Negative Binomial (r,p) i=1 PROPOSITION: The expected value and variance of a Negative Binomial random variable with parameters r and p are E(X) = r 1 - p V(X) =r " Ρ p² Example: You roll a fair six-sided die until you see the third six. What is the probability that this happens on the tenth roll?

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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