F(x)=P{X≤x},(−∞<x<∞) F(x)=P\{X\leq x\},(-\infty<x<\infty) F(x)=P{X≤x},(−∞<x<∞)
如果XXX是连续随机变量, 则
F(x)=∫−∞xf(t) dt F(x)=\int _{-\infty}^{x}f(t) \, dt F(x)=∫−∞xf(t)dt
P{x1<X≤x2}=P{X≤x2}−P{X≤x1}=F(x2)−F(x1) P\{x_{1}<X\leq x_{2}\}=P\{X\leq x_{2}\}-P\{X\leq x_{1}\}=F(x_{2})-F(x_{1}) P{x1<X≤x2}=P{X≤x2}−P{X≤x1}=F(x2)−F(x1)
