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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.

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M91695185

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