# Thread: Fixed points in a permutation, mean and variance

1. ## Fixed points in a permutation, mean and variance

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.

2. Originally Posted by discprobques
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.)
Tell us what you found to be the mean and how it is found.