Question: (9 points) Let f(x, y) = 1/8, 0 y 4, yxy+2, be the joint PDF of X and Y. (a) Sketch the region for

(9 points) Let f(x, y) = 1/8, 0 y 4, yxy+2, be

(9 points) Let f(x, y) = 1/8, 0 y 4, yxy+2, be the joint PDF of X and Y. (a) Sketch the region for which f(x, y) > 0. (b) Find fx(x), the marginal PDF of X. (c) Find fy (y), the marginal PDF of Y. (d) Determine fy|x(y|x), the conditional PDF of Y, given that X = x. (e) Determine fxy (ly), the conditional PDF of X, given that Y = y. (f) Compute E[Y|X = x], the conditional mean of Y, given that X = x. (g) Compute E[XIY = y], the conditional mean of X, given that Y = y. (h) Graph y=E[Y|X = x] on your sketch in part (a). Is y=E[Y|X = x] linear? (i) Graph x =E[X]Y = y] on your sketch in part (a). Is x = EXY y] linear? =

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