397. Given the distribution function $F(x)$ of a random variable $X$. Find the distribution function $G(y)$ of the random variable $Y=3X+2$.

翻译结果如下：

397. Given the distribution function $F(x)$ of a random variable $X$. Find the distribution function $G(y)$ of the random variable $Y=3X+2$.
Solution. By the definition of the distribution function, $G(y)=$ $=P(Y<y)$. Since the function $y=3 x+2$ is increasing, the inequality $Y<y$ holds if the inequality $X<x$ holds, therefore

$$
G(y)=P(Y<y)=P(X<x)=F(x)
$$

From the equation $y=3 x+2$, we express $x$:

$$
x=(y-2) / 3
$$

Substituting (**) into (*), we finally get

$$
G(y)=F[(y-2) / 3]
$$