Chapter 3 - Section 3-4 - Mean and Variance of a Discrete Random Variable - Exercises - Page 77: 3-72

$\mathbb{E}(X)=4.45$ $\operatorname{Var}(X)=1.9975$

$\mathbb{E}(X)=1.5 \times 0.05+3 \times 0.25+4.5 \times 0.35+5 \times 0.2+7 \times 0.15=4.45$ $\mathbb{E}\left(X^{2}\right)=1.5^{2} \times 0.05+3^{2} \times 0.25+4.5^{2} \times 0.35+5^{2} \times 0.2+7^{2} \times 0.15=21.8$ $\operatorname{Var}(X)=\mathbb{E}\left(X^{2}\right)-\mathbb{E}(X)^{2}=1.9975$