例1RV.X的分布律为 0 1 2 Pk 0.30.60.1 求X的分布函数(x)并求P{1<X≤2},F(0.5)及PX=0.5} 解F(x)=PX5x}=∑PX=x} k ≤x x<0. P{X=0}=0.3 0≤x<1, P{X=0+PX=1=0.9,1≤x<2
解 F(x) = P{X x} 例1 R.V. X的分布律为 求X的分布函数F(x)，并求P{1 X 2},F(0.5)及P{X = 0.5}. pk 0.3 0.6 0.1 X 0 1 2 = = x k x P X xk { } = 0, x 0, P{X = 0} 0 x 1, P{X = 0}+ P{X =1} = 0.3, = 0.9, 1 x 2, 1, x 2
P{1<X≤2}=F(2)-F(1)=1-0.9=0.1 或 =P{X=2}. F(0.5=03, P{X=0.5}=0 0.9 0.3
P{1 X 2} P{X = 0.5}= 0. = F(2) − F(1) = 1 − 0.9 = 0.1 = P{X = 2}. 或 F(0.5) = 0.3, O 1 2 x 0.3 0.9 1