设D={(x,y)|x＜y，x＞0，y＞0}={(x,y)|0＜x＜y＜+∞}则：P(X＜Y)=∫∫(D)f(x,y)dxdy=∫∫(D)2e^(-x-2y)·dxdy=∫(0→+∞)dy∫(0→y)2e^(-x-2y)·dx=∫(0→+∞)2[e^(-2y)-e^(-3y)]dy=-e^(-2y)+2/3·e^(-3y) |(0→+∞)=0-(-1+2/3)=1/3
