Solution
Variance of Two Dice
Show the problem again
What is the variance of the sum of two independent fair six-sided dice? Express as a fraction.
Worked solution
The answer is 35/6 ≈ 5.83. For one die, E[X] = 7/2 and E[X²] = 91/6, so Var(X) = 91/6 − 49/4 = 35/12. Variances of independent variables add: Var(sum) = 2 × 35/12 = 35/6. Note that standard deviations do not add: a frequent error.
Source: Standard variance exercise from introductory statistics texts. Statement written for AxiomIQ.