What is the variance of the number obtained on a throw of an unbiased die? 

35/12

Sample Space : S = {1, 2, 3, 4, 5, 6}

The probability distribution is given as : 

E(X) = (1)(1/6) + (2)(1/6) + (3)(1/6) + (4)(1/6) + (5)(1/6) + (6)(1/6)

       = 21/6

E(X²) = (1)²(1/6) + (2)²(1/6) + (3)²(1/6) + (4)²(1/6) + (5)²(1/6) + (6)²(1/6)

         = 91/6

Variance : Var(x) = E(X²) - [E(X)]² = 91/6 - [21/6]²

Var(X) = 35/12