Suppose that we conduct independent Bernoulli trials and record Y , the number of the
Chapter 16, Problem 16.9(choose chapter or problem)
Suppose that we conduct independent Bernoulli trials and record Y , the number of the trial on which the first success occurs. As discussed in Section 3.5, the random variable Y has a geometric distribution with success probability p. A beta distribution is again a conjugate prior for p. a If we choose a beta prior with parameters and , show that the posterior distribution of p | y is beta with parameters = + 1 and = + y 1. b Find the Bayes estimators for p and p(1 p).
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