Question

设随机变量x的概率密度函数为f（x），且f（x）=f（-x）

Answer 1

因为f（x）是随机变量x的概率密度函数
所以
∫f(x)d(x)│(x=-
∞
to
+∞)=1
又因为
f（x）=f（-x）
所以
∫f(x)d(x)│(x=-
a
to
0)=∫f(x)d(x)│(x=0
to
a
)
F(0)=∫f(x)d(x)│(x=-
∞
to
0)=∫f(x)d(x)│(x=0
to
+∞
)=(1/2)*∫f(x)d(x)│(x=-
∞
to
+∞)=1/2
F(-a)=∫f(x)d(x)│(x=-
∞
to
-a)=∫f(x)d(x)│(x=-
∞
to
0)-∫f(x)d(x)│(x=-
a
to
0)=1/2-∫f(x)d(x)│(x=0
to
a
)