1. Assume that the service time for a customer at a bank is exponentially dis- tributed with mean service time 2 minutes. Let X be the total service time for 10 customers. Estimate the probability that X > 22 minutes.
2. Let X1, X2, . . . , Xn be n independent random variables each of which has an exponential density with mean µ. Let M be the minimum value of the Xj . Show that the density for M is exponential with mean µ/n. Hint : Use cumulative distribution functions.