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

[[math]] 1^2 + 2^2 + \cdots + n^2 = \frac{(n)(n+1)(2n+1)}{6}\ . [[/math]]