Question

In: Statistics and Probability

A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...

A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and 1 coin that lands heads with probability 1/4 . A coin is taken from the box at random and flipped repeatedly until it has landed heads three times. Let X be the number of times that the coin is flipped and Y be the probability that the coin lands heads.

(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of Y .

(b) Compute E(X).

(c) Compute var(X).

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