Question

设随机变量X的分布函数为

设随机变量X的分布函数为题目如图

Answer 1

F(x)
=0 ; x,0
=x/2 ; 0≤x<1
=2/3 ; 1≤x<2
=11/12 ; 2≤x<3
=1 ; x≥3
(1) P(X≤3) = F(3) =1
(2) P(X<3) = F(3-) = 11/12
(3) P( X=1) = F(1) - F(1-) = 2/3 - 1/2 = 1/6
(4)P( X>1/2) = P(X≤1/2) = F(1/2) = (1/2)/2 = 1/4
(5) P(2<X<4) = F(4-) -F(2) = 1 - 11/12 = 1/12
(6) P(1≤x <3 ) = F(3-) -F(1-) =11/12 - 1/2 = 5/12

追问

第六小题为什么是1/4

追答

(6) P(1≤x <3 ) = F(3-) -F(1-) =11/12 - 1/2 = 5/12