Example 9. Find the mathematical expectation of a random variable $X$,
uniformly distributed on the interval $[2,8]$.
Solution. The mathematical expectation of a random variable $X$, uniformly distributed on the interval $[\alpha, \beta]$, is defined by formula (3.4.7). Since in this case $\alpha=2, \beta=8$, then

$$
M(X)=\frac{8+2}{2}=5
$$