Suppose that 116 people throw their hats in a box and then each picks one hat at random. Each hat can be picked by only one person, and each assignment of hats to persons is equally likely.
Let and be two random variables. takes the value 856 if the th person selects his/her own hat, and takes the value 0 otherwise. Similarly, takes the value 856 if the th person selects his/her own hat, and takes the value 0 otherwise. Note that ( is not equal to ).
Compute the covariance of and .
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