Solutions should be explained clearly using complete sentences. 1. Let X1, X2. . .. . X, be a sequence of independent exponential random variables with rate parameters A1 , A2. . . . . An, respectively. (a) Prove that the random variable M = min(X1, X2. ..., X,) is an exponential random variable with rate parameter A = >.-, M. (b) Prove that the probability that the minimum A is realized by the random variable X, is