Let X and Y have the joint probability density function f(x, y) = ⎧⎪⎪ ⎨ ⎪⎪⎩ ke−y , if 0 ≤ x ≤ y < ∞, 0, otherwise. (a) (6pts) Find k so that f(x, y) is a valid joint p.d.f. (b) (6pts) Find the marginal p.d.f. fX(x) and fY (y). Are X and Y independent?
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