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1. Given a random permutation of the integers in the set {1, 2, 3, 4, 5}, let X equal the number of integers that are at the correct position. (i) Find the pmf of X. (ii) Find the mgf of X. (iii) Deduce the mean and variance of X. (iv) Find the probability that at least one integer is at the correct position. 2. (i) Let X be a discrete random variable with nonnegative integer values. Show that