Let X1 and X2 be 2 independent exponential random variables each with parameter 1. Let Yn Solution First, find the CDF. P(X1 <= Y and X2 <= Y) = P(X1 <= Y)P(X2 <= Y) = (1 - e-y )(1 - e-y ) = 1 - 2e-y + e-2y Thus, f(x) = 2e-y - 2e-2y Note that 2e-y is in the form of twice the exponential distribution with parameter 1, which has mean 1, and 2e-2y is the exponential distribution with parameter 2, which has mean 1/2 Thus, E(x) = 2(1) - 1/2 = 3/2.