随机变量(x,y)的联合函数为f(x,y)=cxe^-y,0

Question

随机变量(x,y)的联合函数为f(x,y)=cxe^-y,0

Answer 1

f(x,y)=cxe^-y,
由于
S(0,+∞)cxdxS(x,+∞)e^-ydy=1
cS(0,+∞)xdxS(x,+∞)e^-ydy=1
因为S(x,+∞)e^-ydy=-e^-y I(x,+∞)=0-(-e^-x)=e^-x
得
cS(0,+∞)xdxS(x,+∞)e^-ydy
=cS(0,+∞)xe^-xdx
=c[-x*e^(-x)-e^(-x)] I(0,+∞) 分部积分法得
=0-c(0-e^0)
=c
故c=1.