Let X1, X2, ...., X4 be 4 mutually independent random variables, each of which is uniformly distributed on the integers from 1 to k. Let Y denote the minimum of the Xi\'s. Find the probability that Y=1 as a function of k. P(Y = 1) = Find the probability that Y = 2, P(Y = 2) = Solution P(Y=1) = 1 - P(X1>1, X2>1, X3>1, X4>1) P(Y=1) = 1 - ((k-1)/k)^4.