设X-N(3,2^2),求P{2<X<=5};P{X>3};求常数c,使P{X>c}=P{X<=c}
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P(2<X<=5)
=P(X<=5)-P(X<=2)
=P((X-3)/2<=(5-3)/2)-P((X-3)/2<=(2-3)/2)
=P((X-3)/2<=1)-P((X-3)/2<=-1/2)
=Φ(1)-[1-Φ(1/2)]
=Φ(1)+Φ(1/2)-1 查表Φ(1)=0.841，Φ(1/2)=0.691
=0.532
P(X>3)=0.5 因为3是正态分布对称轴
P(X>c)=P(X<=c)=1-P(X>c)
得P(X>c)=0.5 所以c=3
=P(X<=5)-P(X<=2)
=P((X-3)/2<=(5-3)/2)-P((X-3)/2<=(2-3)/2)
=P((X-3)/2<=1)-P((X-3)/2<=-1/2)
=Φ(1)-[1-Φ(1/2)]
=Φ(1)+Φ(1/2)-1 查表Φ(1)=0.841，Φ(1/2)=0.691
=0.532
P(X>3)=0.5 因为3是正态分布对称轴
P(X>c)=P(X<=c)=1-P(X>c)
得P(X>c)=0.5 所以c=3
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