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Problem 8. Let X1, X2, ..., Xn be n i.i.d. exponential random variables with mean 1. (a) Find the pdf of Y = X1 +

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Problem 8. Let X1, X2, ..., Xn be n i.i.d. exponential random variables with mean 1. (a) Find the pdf of Y = X1 + X2+ ...+ Xn. (b) Find the pdf of Z = $1. (c) Are Y and Z independent? (d) Let XM = max; Xi be the maximum of these random variables. What is the joint distribution of Xy and the rest of the random variables

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