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A1. (a) Find the moment generating function of a random variable x ~ N(u,02). (b) Find E(X*]. (c) For u = 0 and a = 1, find E[X|X > 0]. A4. Suppose that in any given time period a certain stock is equally likely to go up 1 unit or down 1 unit, and that the outcomes of different periods are independent. Let x be the cumulative amount the stock goes up in the first two periods, and let Y be the cumulative amount it goes up in the first three periods. Find the correlation between X and Y.

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