What are the mean and variance of the number of fixed elements, that is, elements left in the same position, of a randomly selected permutation of n elements? (Hint: Let X denote the number of fixed points of a random permutation, Write X=X1+X2+...+Xn wherre Xi=1 if the permuation fixes the ith element and Xi=0 otherwise.)
A google search and the solution in the book I'm using says the variance is 1 but neither provides a proof. I got (n-1)/n when I did it. Does someone know how to get 1? Thanks.