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Suppose X1 and X2 are independent expon(λ) random variables. Let Y = min(X1, X2) and Z...

Suppose X1 and X2 are independent expon(λ) random variables. Let Y = min(X1, X2) and Z = max(X1, X2).

(a) Show that Y ∼ expon(2λ)

(b) Find E(Y ) and E(Z).

(c) Find the conditional density fZ|Y (z|y).

(d) FindP(Z>2Y).

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