(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Generalize: For arbitrary 0 < p < 1, show that the method giving a and b produces the minimum length interval.

Hint: It might be helpful to use local extrema for the inverse function of the distribution function.

2. Relevant equations

The method is is talking about is locating the z scores using (1-p)/2 and [1-(1-p)/2]

3. The attempt at a solution

Let a be the area on the tail end of the distribution not included in p

Let b be the other end so that

a+b=1-p and b=1-p-a

Then the points A and B are the end points of the interval containing p.

B-A = (F^-1)(p+a)-(F^-1)(a)

This is where I am stuck. I know f(y). So d/dy(F(y))=f(y) and then (f^-1)'(y)=1/(f'(f^-1)(y))

I am not sure how to proceed.

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# Homework Help: Statistics:minimizing an interval for a standard normal distribution

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