A number is chosen at random from the integers 1, 2, 3, , n Let X be the number chosen Show that E(X) (n 1) 2 and V (X) (n minus 1)(n 1) 12 Hint The following identity may be useful 12 22 12 (n)(n 1)(2n 1) 6

Question: A number is chosen at random from the integers 1, 2, 3, . . . , n. Let X be the number chosen. Show that

A number is chosen at random from the integers 1, 2, 3, . . . , n. Let X be the number chosen. Show that E(X) = (n+1)/2 and V (X) = (n−1)(n+1)/12. Hint: The following identity may be useful:

12 +22 + +12 = (n)(n +1)(2n + 1) 6

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