An experiment consists of casting an eight-sided die (numbered 1 through 8) and observing the number that appears uppermost. Find the mean and variance of this experiment.
A) m = 4.16, Var (X) = 4.99
B) m = 4.50, Var (X) = 5.25
C) m = 4.39, Var (X) = 4.54
D) m = 4.39, Var (X) = 4.99

Question

Quizplus · Accepted Answer

The mean (m) of a fair eight-sided die is calculated as the sum of all outcomes divided by the number of outcomes, which is (1+2+3+4+5+6+7+8)/8 = 36/8 = 4.5. The variance (Var(X)) is calculated using the formula for the variance of a uniform distribution over n outcomes, Var(X) = (n^2 - 1) / 12, which for an eight-sided die (n=8) gives Var(X) = (8^2 - 1) / 12 = 64 - 1 / 12 = 63 / 12 = 5.25.

An Experiment Consists of Casting an Eight-Sided Die (Numbered 1