設(shè)隨機(jī)變量XY的概率密度為f(x,y)=be^[-(x+y)],0

數(shù)學(xué)人氣：785 ℃時(shí)間：2019-08-19 00:17:18

優(yōu)質(zhì)解答

∫∫be^[-(x+y)]dxdy=1,可得b=e/(e-1)
f(x)=∫be^[-(x+y)]dy=be^(-x),0f(y)=∫be^[-(x+y)]dx=e^(-y),0因?yàn)閒(x,y)=f(x)*f(y),所以X,Y相互獨(dú)立
求U=max(x,y)
F(u)=P(U<=u)=P(max(X,Y)<=u)=P(X<=u,Y<=u)=P(X<=u)P(Y<=u)
可得U=max(x,y)的分布函數(shù)如下：
當(dāng)u<=0時(shí),F(u)=0
當(dāng)0當(dāng)1<=u時(shí),F(u)=1-e^(-u)
可得U=max(x,y)的概率密度函數(shù)如下：
f(u)=2be^(-u)*[1-e^(-u)],0f(u)=e^(-u),u>=1
f(u)=0,u取其他值
解畢