数学试题讲解

设随机变量

X_{1}

与

X_{2}

相互独立, 其分布函数分别为

\begin{aligned} F_{1} (x) = {\begin{cases} 0, & x < 0, \\ \frac{1}{2}, & 0 ⩽ x < 1, F_{2} (x) = \int_{- \infty}^{x} \frac{1}{\sqrt{2 π}} e^{- \frac{t^{2}}{2}} d t, - \infty < x < + \infty, \\ 1, & x ⩾ 1, \end{cases} \end{aligned}

则

X_{1} + X_{2}

的分布函数

F (x) = ()

F_{1} (x) + F_{2} (x)

\frac{1}{2} F_{1} (x) + \frac{1}{2} F_{2} (x)

\frac{1}{2} F_{1} (x) + \frac{1}{2} F_{2} (x - 1)

\frac{1}{2} F_{2} (x) + \frac{1}{2} F_{2} (x - 1)