Question

设二维随机变量(X,Y)的概率密度为f(x,y)=kx(x-y),0

Answer 1

1=∫(0~2)∫(-x~x) kx(x-y)dydx

1=∫(0~2) kx(xy-y^2/2)|(-x~x) dx

1=∫(0~2)2kx^3dx

1=2kx^4/4(0~2)

1=8k

k=1/8

画图可知范围

fy(y)=∫(|y|~2) kx(x-y)dx

=kx^3/3-kyx^2/2 | |y|~2

=1/8(8/3-2-(y^2|y|/3-y^3/2))

=1/12-y^2|y|/24+y^3/16

(-2