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Question 1 (8 points) Random variables X and Y have joint PDF C - -1fx,Y (x,y) = 0 otherwise. (a) Find the constant c. (b) Find fy (y) and fxjy(x(y). (c) Find E[Y]. (d) Find XM (Y), the minimum mean square error (MMSE) estimator for X given a single sample of Y. Question 2 (7 points) We flip a coin n times and count how many times we observe "heads"; let Pn be the estimated probability of heads (the relative frequency of occurence). Assume the coin is fair; the true probability of heads is p = 0.5. (a) Find E[Pn] and Var [Pn].

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