设密度函数为f(x),分布函数为F(x)
P(X<=Y)=(x<=y积分)∫∫(x<=y积分)f(x)f(y)dxdy
=∫(-∞,+∞)f(x)dx∫(x,+∞)f(y)dy
=∫(-∞,+∞)f(x)[1-F(x)]dx
=∫(-∞,+∞)[1-F(x)]dF(x)
=-[1-F(x)]^2/2|(-∞,+∞)
=1/2