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3. Suppose the random variable X has a continuous uniform distribution on (0, 1). [4] (a) Let Y = 3 In(1/X). Find the probability density function (p.d.f.) fy(y) of Y. [3] (b) Derive the moment generating function (m.g.f.) My (t) of Y. [3] (c) Calculate E(Y) and Var(Y). Make sure to show your work. [10] 4. Suppose there are 20 different types of collectible cards and suppose that each time you buy a card, it is equally likely to be any one of the 20 types. Let X be the number of types of cards you still do not have after buying 10 random cards. Find E(X) and Var(X). (Hint: Define indicator variables X1, X2, ... X2, where Xi = 1, if type i is not obtained 0, otherwise and remember that the number of pairs (i, j) with i 0.5