12. Expectation

Question 1

Using the definitions with the probability function given in Table 11.1, we have

E(X) = 0.125×0 + 0.375×1 + 0.375×2 + 0.125×3 = 1.5.

var(X) = 0.125(0 - 1.5)² + 0.375(1 - 1.5)² + 0.375(2 - 1.5)² + 0.125(3 - 1.5)² = 0.75,

so sd(X) = √0.75 = 0.866.

Question 2

Mathematica was used to calculate these (as shown below) using the definitions from Section 12.4, giving E(X) = 170 cm and sd(X) = 11.547 cm.