398. Given the distribution function $F(x)$ of a random variable $X$. Find the distribution function $G(y)$ of the random variable $Y=-(2 / 3) X+2$.
Solution. By the definition of the distribution function,

$$
G(y)=P(Y<x), \text{ therefore } G(y)=P(Y<x).
$$

Events $X<x$ and $X>x$ are complementary, so the sum of their probabilities is one: $P(X<x) + P(X>x) = 1$. Therefore,

$$
P(X>x)=1-P(X<x)=1-F(x) \text {; }
$$

hence,

$$
G(y)=1-F(x)
$$

From the equation $y=-(2 / 3) x+2$, solve for $x$:

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

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

$$
G(y)=1-F[3(2-y) / 2]
$$