Question: Let X = (X1 X2) be a 1 X 2 random vector. (a) Suppose X has a mg'f of the form MX((t1 752)) = 9(t1)h(t2)

Let X = (X1 X2) be a 1 X 2 random vector. (a) Suppose X has a mg'f of the form MX((t1 752)) = 9(t1)h(t2) Where g and h are real functions dened throughout a neighborhood of zero. Assume 9(0) = 1. (i) Show h(0) = 1. (ii) Show 9 is the mgf of X1. (iii) Are X1 and X2 necessarily independent? Justify your answer. (b) Suppose X has the mgf Mx((t1 t2 = 8t1+t2 (all t1 and t2) Explain Why X has a multivariate normal distribution, and determine the parameter values of that distribution

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