The N Candidates for a Store Manager Have Been Ranked $$p ( x ) = \left\{ \begin{array} { l l } 1 / n & x = 1,2,3 \ldots , n \\0 & \text { otherwise }\end{array} \right.$$

Essay

The n candidates for a store manager have been ranked 1,2,3,…,n. Let X = the rank of a randomly selected candidate, so that X has pmf $$p ( x ) = \left\{ \begin{array} { l l } 1 / n & x = 1,2,3 \ldots , n \\0 & \text { otherwise }\end{array} \right.$$ (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.]