What is the variance of the number obtained on a throw of an unbiased die?
Answer & explanation
Correct answer: option 4
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