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1. Consider the joint distribution fXY (x, y) = k · x y (1) over the...

1. Consider the joint distribution fXY (x, y) = k · x y (1) over the domain 0 < x < 1, 0 < y < 1, for some k > 0. (a) What value should k have for f to be a proper density? (b) Find the marginal densities of X and Y . Hint: x y = exp[y · log(x)]. (c) Find the mean of Y . (d) Find the conditional mean of Y , given X

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