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.]

Question

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.]

Quizplus · Accepted Answer

The Answer of 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.]

The N Candidates for a Store Manager Have Been Ranked p(x)={1/nx=1,2,3…,n0 otherwise p ( x ) = \left\{ \begin{array} { l l } 1 / n & x = 1,2,3 \ldots , n \\0 & \text { otherwise }\end{array} \right.p(x)={1/n0​x=1,2,3…,n otherwise ​

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