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2· Let 0 < p < 0.5. Assume that there are two biased coins. The 1st coin shows heads with probability p and the second coin shows heads with probability q, where q-1-p. Consider the following two stage experiment. First, select one of the two coins at random, with each coin being selected with probability 1/2, and then flip the selected coin n times. Let X be the number of times heads shows. Compute the p.m.f., mean (expected value), and variance of X.

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2 AnsweR heaae hot ac biased coins Aesecond com shous head swith probabi lit】 Noolete le number of tines heals shous. Then He, coin s pipped ntes iVe te poabili Jiscrete andon variables 0 Some va lue た0 n-Xd되 X-I 2.

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