Example 5. Find the mathematical expectation of the random variable $Y=2X+7$, given that $M(X)=4$.
Solution. Using formulas (2.4.10), (2.4.11), (2.4.12), we find

$$
\begin{aligned}
& M(Y)=M(2 X+7)=M(2 X)+M(7)= \\
& =2 M(X)+7=2 \cdot 4+7=15
\end{aligned}
$$