Question

设随机变量X~N(0,1),Y=|x|,求Y的概率密度函数

Answer 1

∵ Y的分布函数为 FY ( y)=P (Y≤y )=P ( | X |≤y)
当y0时：ψ( y)= [FY ( y)]' = [(-y,y)(1/√2π）e^-(x^2/2)dx]＇=√(2/π)e^-(y^/2)