设随机变量X 的概率密度为f(x)=(1/π^2)e^(-x^2+2x-1),求E(x)

题目

设随机变量X 的概率密度为f(x)=(1/π^2)e^(-x^2+2x-1),求E(x)

答案

f(x) = (1/π^2)e^[-(x-1)^2]
= [1/π^(3/2)]{[1/π^(1/2)]e^[-(x-1)^2]}
所以x ~ [1/π^(3/2)] N(1,1/2)
E(x) = [1/π^(3/2)]μ
= 1/π^(3/2)