Question: 2. Let X1, X2 be independent exponential random variables with common parameter A. (a) Find the joint pdf of Z1 = x,ex, and Z2 =

2. Let X1, X2 be independent exponential random variables with common

2. Let X1, X2 be independent exponential random variables with common parameter A. (a) Find the joint pdf of Z1 = x,ex, and Z2 = X1 + X2. (b) Show that Z1 and Z2 are independent. (c) Obtain the pdf of W = X1 + X2 using three different methods: 1) result of the 2-2 transformation obtained in (a). 2) first derive the formula fx+y(t) = Jfxy (x, t - x)dx and then use it to find fw (t). 3) first find the cdf of W and then differentiate

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