Question: What is the variance of the number of fixed elements, that is, elements left in the same position, of a randomly selected permutation of n elements?
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 ))).