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In exercises let X and Y be independent random variables. Let Z = Y - X. Let A = [|Y - X| ≤ 1]. Find (i) P[A|X = 1], (ii) FZIX(0|1), (iii)fzlx(0|1), (iv) P[Z ≤ 0|A].

If X and Yare each exponentially distributed with parameter λ = 1.

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