Example 11. Find the mathematical expectation of the random variable
$X$, the density of which is determined by the function $p(x)=0.2 e^{-0.2 x}$ for $x \geq 0$.
Solution. Since in this case $\alpha=0.2$ and $M(X)=\frac{1}{\alpha}$, then

$$
M(X)=\frac{1}{2 / 10}=\frac{10}{2}=5, \quad M(X)=5
$$