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Q1. Suppose that the joint distribution of X and Y is standard bivariate normal with correlation p. Y - pX (a) Let U = X

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Q1. Suppose that the joint distribution of X and Y is standard bivariate normal with correlation p. Y - pX (a) Let U = X and V = VI- p2 Show that U and Vare uncorrelated and that Var (V ) = 1. (b) Now let W = X. Find the r moment of W. You may use the moment generating function of a standard normal without proof.] [40 marks]

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