概率论与数理统计三题求解答
发布网友
发布时间：2022-05-06 01:05
共1个回答
热心网友
时间：2022-06-28 10:32
当x<-1时，F(x)=0
当-1≤x<0时，F(x)=0.2
当0≤x<2时，F(x)=0.2+0.5=0.7
当2≤x时，F(x)=1
P{-1<=X<=1}=F(1)-F(-1)+P{X<=-1}=0.7-0.2+0.2=0.7
EX=-1*0.2+2*0.3+0*0.5=0.4
E（-3X+1）=-3EX+1=-1.2+1=-0.2
第二题
f(x)=[F(x)]'=1/(1+x)^2 x≥0
f(x)=0 x<0
P{x<3}=F(3)=3/4
P{-2<x<5}=P{0<x<5}=F(5)=5/6
第三题
EX=∫(-无穷,+无穷)xf(x)dx=∫(-1,0)0.2xdx+∫(0,1)(0.2x+1.2x^2)dx
=-0.1+0.1+0.4=0.4
EX^2=∫(-无穷,+无穷)x^2f(x)dx
=∫(-1,0)0.2x^2dx+∫(0,1)(0.2x^2+1.2x^3)dx
=-1/15+1/15+0.3=0.3
DX=EX^2-(EX)^2=0.3-0.4*0.4=0.14
