Suppose that three male students are making telephone calls to their girlfriends. Let X1, X2, X3 denote the times of their phone calls. Suppose that the Xj's are independent Exponential random variables, each with expected value 20 minutes.
a. Find the density of X(1), the first order statistic. (Easy check: X(1) is the minimum of three independent Exponentials, so we remember that X(1) is Exponential too.)
b. Find the probability that none of the calls are less than 12 minutes long, i.e., they all exceed 12 minutes.
c. Find the probability that two or more of the calls are less than 23 minutes each.