Problem 37E
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 (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.]
Step-by-Step Solution:
Answer Step 1 of 3 E(x)=xp(x) =x(1/n) =(1/n)n(n+1)/2 here x means The sum of the first n positive integers i.e. n(n + 1) /2 =(n+1)/2 Step 2 of 3 E(x )=x p(x) 2 =x (1/n) =(1/n) n(n + 1)(2n + 1)/6 =(n + 1)(2n + 1)/6
Step 3 of 3
