5. A geometric distribution with parameter p has probability mass function f(x) = (1-p)-1p, x =...

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5. A geometric distribution with parameter p has probability mass function f(x) = (1-p)-1p, x = {1, 2,...}. (a) Show that the Jeffreys prior for this distribution is the following improper prior. f(p) x p(1 - p)-0.5 (Hint: For the geometric, EX = 1/p.) (b) We observe iid realizations X1,..., Xn of a random variable X with a geometric distri- bution with parameter p. Find the posterior distribution of p using the Jeffreys prior from part (a). 5. A geometric distribution with parameter p has probability mass function f(x) = (1-p)-1p, x = {1, 2,...}. (a) Show that the Jeffreys prior for this distribution is the following improper prior. f(p) x p(1 - p)-0.5 (Hint: For the geometric, EX = 1/p.) (b) We observe iid realizations X1,..., Xn of a random variable X with a geometric distri- bution with parameter p. Find the posterior distribution of p using the Jeffreys prior from part (a).