Deriving the confidence interval \(\displaystyle{P}{\left(-\Phi^{{-{1}}}_\alpha{ < }{X}{

nomadzkia0re

nomadzkia0re

Answered question

2022-03-27

Deriving the confidence interval
P(Φα1<X<Φα1)=12α
Let PN(0,1)
 P(Φα1<X<Φα1)  (1) P(X<Φα1)P(X<Φα1) P(A<X<B)=P(X<B)P(X<A)(2) Φ(Φα1))Φ(Φα1)) P(X<A)=Φ(A)(3) Φ(Φα1))(1Φ(Φα1))) Φ(x)=1Φ(x)(4) α1+α f(f1)=id(5) 1×(12α)  (6)

Answer & Explanation

Pubephenedsjq

Pubephenedsjq

Beginner2022-03-28Added 11 answers

Note that for α<0.5, you get ϕ1(a)<0.
Hence, 12α0 so for sure α0.5. Then,
P(ϕ1(α)<X<ϕ1(α))=1ϕ(ϕ1(α))ϕ(ϕ1(α))=12α

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