In: Statistics and Probability
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).