2. Suppose 10 people toss their hats into a box and then take turns drawing hats at random, so each person ends up with one hat. How many possible permutations of the hats are there? Assume that each such permuation is equally likely. Let Si be one if the ith person gets her own hat, zero otherwise. (a) Calculate mean and variance of Si. (b) Calculate the covariance of Si and S; when i + j. (c) Let S be the number of people who get their own hat. Calculate the mean and variance of S.

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