二维随机向量(X,Y)概率密度函数为 f(x,y)=2e^[-(2x+y)],x>=0,y>=0 =0,其它求概率P{Y

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二维随机向量(X,Y)概率密度函数为f(x,y)=2e^[-(2x+y)],x>=0,y>=0=0,其它求概率P{Y二维随机向量(X,Y)概率密度函数为f(x,y)=2e^[-(2x+y)],x>=0

二维随机向量(X,Y)概率密度函数为 f(x,y)=2e^[-(2x+y)],x>=0,y>=0 =0,其它求概率P{Y
二维随机向量(X,Y)概率密度函数为 f(x,y)=2e^[-(2x+y)],x>=0,y>=0 =0,其它求概率P{Y

二维随机向量(X,Y)概率密度函数为 f(x,y)=2e^[-(2x+y)],x>=0,y>=0 =0,其它求概率P{Y
P{Y≤X}=∫∫f(x,y)dxdy
y≤x
=∫(0--+∝)dx∫(0-->x)2e^[-(2x+y)]dy
=∫(0--+∝)dx∫(0-->x)2e^[-2x-y)]dy
=2∫(0--+∝)e^(-2x)dx∫(0-->x)e^(-y)]dy
=2∫(0--+∝)e^(-2x)[1-e^(-x)]dx
=2∫(0--+∝)e^(-2x)-e^(-3x)]dx
=1-2/3
=1/3

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二维随机向量(X,Y)概率密度函数为 f(x,y)=2e^[-(2x+y)]，x>=0,y>=0 =0,其它
于是P{Y<=X}=∫∫{Y<=X}f(x,y)dxdy=∫(-∞,+∞)dx∫(-∞,x)f(x,y)dy
=∫(-∞,0)dx∫(-∞,x)f(x,y)dy+∫[0,+∞)dx∫(-∞,x)f(x,y)dy
=∫(0,+∞)dx∫(-∞,x)f(x,y)dy
=∫(0,+∞)[∫(-∞,0)f(x,y)dy+∫[0,x)f(x,y)dy]dx
=∫(0,+∞)dx∫[0,x)f(x,y)dy
=∫(0,+∞)dx∫[0,x)2e^[-(2x+y)]dy
=-∫(0,+∞)2e^[-(2x+y)]|[0,x)dx
=∫(0,+∞)[2e^(-2x)-2e^(-3x)]dx
=-e^(-2x)|(0,+∞)+(2/3)e^(-3x)|(0,+∞)
=1-(2/3)
=1/3

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二维随机向量(X,Y)概率密度函数为 f(x,y)=2e^[-(2x+y)],x>=0,y>=0 =0,其它 求概率P{Y

二维随机向量(X,Y)概率密度函数为 f(x,y)=2e^[-(2x+y)],x>=0,y>=0 =0,其它求概率P{Y