设X~N(1,4),求F(5),P｛0＜X＜=1.6},P｛|X-1|＜=2}
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随机变量X服从N(1,4)，
则有(X-1)/2~N(0,1)，
所以
P(0<X≤1.6)
=P(-0.5≤(X-1)/2<0.3)
=Φ(0.3)-Φ(-0.5)
=Φ(0.3)-[1-Φ(0.5)]
=0.6179-(1-0.6915)
=0.3094
P｛|X-1|＜=2}
= P{-2<=x-1<=2}
= P(-1<=(x-1)/2<=1)
= Φ(1)-Φ(-1)
= 2Φ(1)- 1
= 2*0.8413 - 1
= 0.6826
则有(X-1)/2~N(0,1)，
所以
P(0<X≤1.6)
=P(-0.5≤(X-1)/2<0.3)
=Φ(0.3)-Φ(-0.5)
=Φ(0.3)-[1-Φ(0.5)]
=0.6179-(1-0.6915)
=0.3094
P｛|X-1|＜=2}
= P{-2<=x-1<=2}
= P(-1<=(x-1)/2<=1)
= Φ(1)-Φ(-1)
= 2Φ(1)- 1
= 2*0.8413 - 1
= 0.6826
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