Suppose X₁ and X₂ have the joint par f(x1, x₂) fw (w) For constants w₁ > 0 and w₂ > 0, let W = W₁X₁ + W₂X2. (a) Show that the pdf of W is = { 0 = elsewhere. е-x¹е-x2 { x1 > 0, x₂ > 0 elsewhere. W1-W2 0 1 · (e-w/w₁ 1- e-w/w₂) w > else (b) Verify that fw(w) > 0 for w > 0. (c) Note that the pdf fw(w) has an indeterminate form when w₁ = W₂. Rewrite fw(w) using h defined as w₁ - W₂ = h. Then use l'Hôpital's rule to show that when w₁ = W₂, the pdf is given by fw(w) = (w/w) exp{-w/w₁} for w> 0 and zero

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