Let X be the number of coin tosses until heads is obtained. Suppose that the probability of heads is unknown in the sense that we consider it to be a random variable Y ∈ U (0, 1).
(a) Find the distribution of X (cf. Problem 3.8.48).
(b) The expected value of an Fs-distributed random variable exists, as is well known. What about E X?
(c) Suppose that the value X = n has been observed. Find the posterior distribution of Y , that is, the distribution of Y | X = n.