数学
设X~N(3,4),试求(1)P(2

2019-05-30

设X~N(3,4),试求(1)P(2
优质解答
X~N(3,4),则[(x-3)/2]~N(0,1),所以P(2<X≤5)=P(-0.5<[(X-3)/2]≤1)=1-P(x≤-0.5)-P(X>1)=1-0.3085-0.1587=0.5328,P(-4<X≤10)=P(-3.5<[(X-3)/2]≤3.5)≈1,P(|X|>2)=P(X>2) P(X<-2)=P(X>-0.5) P(X<-2.5)=0.6915 0.0062=0.6977,P(X>3)=P([(X-3)/2]>0)=0.5,关于第二问,必然是P(X>c)=0.5,因为知道P([(X-3)/2]>0)=0.5,所以c=0×2 3=3 X~N(3,4),则[(x-3)/2]~N(0,1),所以P(2<X≤5)=P(-0.5<[(X-3)/2]≤1)=1-P(x≤-0.5)-P(X>1)=1-0.3085-0.1587=0.5328,P(-4<X≤10)=P(-3.5<[(X-3)/2]≤3.5)≈1,P(|X|>2)=P(X>2) P(X<-2)=P(X>-0.5) P(X<-2.5)=0.6915 0.0062=0.6977,P(X>3)=P([(X-3)/2]>0)=0.5,关于第二问,必然是P(X>c)=0.5,因为知道P([(X-3)/2]>0)=0.5,所以c=0×2 3=3
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