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Math Help - Fixed points in a permutation, mean and variance

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    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.
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    Quote Originally Posted by discprobques View Post
    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.
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