Question

高数题求解

Answer 1

P(1<X<3) =0.3413
P( (1-1)/2<Z <(3-1)/2 ) =0.3413
P(0<Z<1) =0.3413

P(Y<0)
=P(Z<(0-1)/1)
=P(Z<1)
=P(0<Z<1)+0.5
=0.3413+0.5
=0.8413

追问

这个我没看懂

0到1也是0.3413？什么意思？不是应该-1到1吗

追答

P(1<X<3) =0.3413
P( (1-1)/2<Z <(3-1)/2 ) =0.3413
P(0<Z<1) =0.3413 (1)

P(Y<0)
=P(Z<(0-1)/1)
=P(Z<1)
=P(0<Z<1)+0.5
=0.3413+0.5 ( from (1) P(0<Z<1) =0.3413 )
=0.8413

追问

这什么意思？你只是复制了一遍啊

追答

根据
P(1<X<3) =0.3413

计算出
P(0<Z<1) =0.3413

P(Y<0)
=P(Z<(0-1)/1)
=P(Z<1)
=P(0<Z<1)+0.5
=0.3413+0.5
=0.8413

追问

正确答案0.1587

追答

P(Y-1)
=1-[ P(0<Z<1) +0.5) ]
= 1- 0.3413-0.5

=0.1587

追问

你这个过程我看不懂啊，能不能解释一下

追答

P(Z>-1)
=P(-10)
=P(00)
=P(Z-1) (P(Z-1) =1 )
=1-[ P(0<Z<1) +0.5) ] ( from (2) )
= 1- 0.3413-0.5

追问

Z表示什么

追答

X~N(μ, δ^2)

Z =(X-μ)/δ
Z ~N(0,1)