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Suppose a fair coin is flipped 5 times. Denote heads by 1 and tails by 0. Therefore, each realization of this

random trial can be represented as a random sequence of zeros and ones of size 5. Define the random variable X to be the size of the largest consecutive subsequence of ones. For example, if the observed sequence is 10110, then X = 2.

(a) Find the p.m.f of X.

(b) Find the probability that the second coin is a head given that X = 3. 

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