Question

Suppose that 84 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 521 if the th person selects his/her own hat, and takes the value 0 otherwise. Similarly,  takes the value 521 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 .

Round your answer to five decimal digits after the decimal point.

Answer 1

Total number of people throw their hate in a box = N =84