#### 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.