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若随机变量x的分布函数为F（x)=a+barctanx,则a=?

2025-03-15 10:41:22

推荐回答（1个）

回答1：

对于分布函数有f(x)=a+barctanx
f(-∞)=a+b(-π/2)=0
f(+∞)=a+b(π/2)=1
a=1/2,b=1/π
即f(x)=1/2+arctanx/π
f(1)-f(-1)=1/2+arctan(1)/π-（1/2+arctan(-1)/π）=1/2
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