随机变量xy的概率密度fxy=1+sinxsiny

Question

设X和Y的联合概率密度为f(x,y)=(1/2π)(1+sinxsiny)e^((x^2+y^2)/-2) X和Y都是负无穷大到正无穷大
求X和Y的边缘概率密度,

Answer 1

f(x)=(1/(2π)^(1/2))e^(-(x²+y²)/2)
f(y)=(1/(2π)^(1/2))e^(-(x²+y²)/2)