An Introduction to Probability and Statistical Inference, 2nd Edition

Chapter 3

Section 3.1

1.2 

(i) EX = 0, $E{X}^2=c^2$, and $\text{Var}\left(X\right)=c^2.$

(ii) $P(|X-EX|\le c)=P(-c\le X\le c)=P(X=-c,X=c)=1=\frac{c^2}{c^2}=\frac{\text{Var}(X)}{c^2}.$

1.4 If Y is the net loss to the company, then EY = $200, and if P is the premium to be charged, then the expected profit is P − EY = P − 200 = 100, so that P = $300.

1.6 $\text{Var}\left(X\right)=E{X}^2-{\left(EX\right)}^2$ by expanding and taking expectations. Also, ...