Question

一道概率论问题,X和Y相互独立且都服从N(0,σ^2),求随机变量Z=根号下X^2+Y^2的概率密度,还有它的期望值,

Answer 1

f(x)=(1/(根号(2π)σ)e^(-x^2/(2σ^2))

f(y)=(1/(根号(2π)σ)e^(-y^2/(2σ^2))

因为X,Y独立,所以f(x,y)=f(x)*f(y)=(1/(2πσ^2)e^(-(x^2+y^2)/(2σ^2))

Z=根号下X^2+Y^2

当z