What is the variance of the number of fixed elements, that
Chapter 6, Problem 6.4.37(choose chapter or problem)
What is the variance of the number of fixed elements, that is, elements left in the same position, of a randomly selected permutation ofn elements? [Hint: Let X denote the number of fixed points of a random permutation. Write X = X, + X2 + . . . + Xn, where Xi = 1 if the permutation fixes the ith element and Xi = 0 otherwise.] The covariance of two random variables X and Y on a sample space S, denoted by Cov(X, y), is defined to be the expected value of the random variable (X - E(X (Y - E(Y . That is, Cov(X, Y) = E X - E(X (Y - E(Y ).
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