2 (30 points) Let X1 and X2 have the joint pdf 6x2 0x2x1 1 f(x1, x2) 0 elsewhere (a) Find the marginal pdf of X, i e , fi(x1) (b) Find the conditional pdf of X2 given X x, i e , f2 1 (x2 x1) (c) Find the conditional mean of X2 given X x1, i e , E(X2 x1) (d) Let Y E(X2 X1) Find the cdf of Y, i e , G(y) P(Y y) (e) Find the pdf, mean, and variance of Y (f) Find the marginal pdf of X2 Compare E(Y) and Var(Y) with E(X2) and Var(X2)

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2. (30 points) Let X1 and X2 have the joint pdf: 6x2 0x2x1 <1 f(x1, x2) = { 0 elsewhere. (a) Find the marginal

2. (30 points) Let X1 and X2 have the joint pdf: 6x2 0x2x1

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