试题分享

试题

设连续型随机变量 $X$ 的分布函数为 $F(x)$ ，且 $F(0)=0$ ，则下列函数可作为分布函数的是

$\text{A.}$ $G_1(x)=\left\{\begin{array}{cc}1+F\left(\frac{1}{x}\right), & x>1, \\ 0, & x \leqslant 1 .\end{array}\right.$ $\text{B.}$ $G_2(x)=\left\{\begin{array}{cc}1-F\left(\frac{1}{x}\right), & x>1, \\ 0, & x \leqslant 1 .\end{array}\right.$ $\text{C.}$ $G_3(x)=\left\{\begin{array}{cc}F(x)-F\left(\frac{1}{x}\right), & x>1, \\ 0, & x \leqslant 1 .\end{array}\right.$ $\text{D.}$ $G_4(x)=\left\{\begin{array}{cc}F(x)+F\left(\frac{1}{x}\right), & x>1, \\ 0, & x \leqslant 1 .\end{array}\right.$