37. The n candidates for a job have been ranked 1, 2, 3, . . . , n. Let X
the rank of a randomly selected candidate, so that X has pmf p(x)
{ 1/n x
1, 2, 3, . . . , n 0 otherwise

(this is called the discrete uniform distribution). Compute E(X) and V(X) using the shortcut formula. [Hint: The sum of the first n positive integers is n(n 1)/2, whereas the sum of their squares is n(n 1)(2n 1)/6.]