Let X1~ exp(1) and X2 ~ exp(1) be independent and identically-distributed exponential random variables with rate...

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Let X1~ exp(1) and X2 ~ exp(1) be independent and identically-distributed exponential random variables with rate...

Let X1~ exp(1) and X2 ~ exp(1) be independent and identically-distributed exponential random variables with rate 1. Let: Y = X1 + X2 , Z = X1 − X2 (a) What is the cdf of X1? (b) What is the joint pdf of (X1, X2)? (c) What is the joint pdf of (Y, Z)? (d) What is the marginal pdf of Z?

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