Question

设X~N(3,4),求(1)P{2<X<=5}(2)P{-4<X<=10}(3)P{|X|>2}(

设X~N(3,4),求(1)P{2<X<=5}(2)P{-4<X<=10}(3)P{|X|>2}(4)P{X>-1}

Answer 1

作变换t=(x-3)/2,
(1)P{2<x<=5}=Φ{-1/2<t<1}=Φ(1)-Φ(-1/2)=Φ(1)-[1-Φ(1/2)]=0.841345+0.691463-1=0.532808.
P{|x|>2}=P{x>2,或x<-2}=Φ{t>-1/2或t<-5/2}=Φ(-5/2)+1-Φ(1/2)=2-Φ(1/2)-Φ(5/2)
=2-(0.691463+0.993790)=0.314747.
(2)c=3.
(3)P(x>d}=Φ[t>(d-3)/2]=1-Φ[(d-3)/2]>=0.9,
∴Φ[(d-3)/2]<=0.1,
(d-3)/2<=-1.28,
d<=0.44,
d至多是0.44(近似值）。
满意请采纳。