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Bayes rule for several discrete and one continuous r.v. You are given a coin with prior random bias P ~ Unif [0, 1]. To obtain more information about the bias of the coin, you flip it 10 times. Let Yi = 1, i = 1, 2, ..., 10, if the outcome of the ith coin flip is a heads and Ya = 0 if it is tails and let X be the number of heads you obtain. (a) For Li yi = k, show that fPly1,Y2,...,Yo (P y1, y2, . . . , y10) = fpIx (p|k), i.e., the conditional pdf of P given Y1, ..., Y10 depends only on the number of heads k. (b) Assuming that k = 9, find and sketch the a posteriori pdf of P, i.e., fpix (P|9). Remark: The pdf of the form fx (k) = c.x-1(1 - x)-1 for a, b > 0 and 0