Statistics for Maintenance Modelling: Basic Probability Concepts

# Variance for Random Variables¤

The variance for discrete and continuous random variables is given as:

Discrete random variable with a probability mass function p(x) | Continuous variance of a random variable X, with expected value

Alternatively, often the easiest way to calculate the variance for both discrete and continuous random variables is by the formula:

Var ( X ) = E [ X 2 ] - (E [ X ]) 2

Can you calculate Var(X) if X represents the outcome when a die is rolled? Recall that when you calculated E[X] for rolling a die, it was 7/2. Type your answer into the textboxes in the fraction format indicated and click the "Check Answer" button. Click the "Hint" button for some help in working out the answer.

| Var(X) = /

Yes, that's right, Var(X) =35/12. Since we already knew E[X], we had to calculate E[X 2] = 12(1/6) + 22(1/6) + 32(1/6) + 42(1/6) + 52(1/6) + 62(1/6) = 91/6

Var(X) = 91/6 - (7/2)2 = 35/12

No, that's not right, Var(X) = 35/12. Since we already knew E[X], we had to calculate E[X 2] = 12(1/6) + 22(1/6) + 32(1/6) + 42(1/6) + 52(1/6) + 62(1/6) = 91/6

Var(X) = E[X 2] - E[X] 2 = 91/6 - (7/2)2 = 35/12