Question

Comparing Quantiles

1 point possible (graded)

Let Z∼N(0,1). Then Z2∼χ21.

The quantile qα(χ21) of the χ21−distibution is the number such that

P(Z2>qα(χ21))=α.

Find the quantiles of the χ21 distribution in terms of the quantiles of the normal distribution. That is, write qα(χ21) in terms of qα′(N(0,1)) where α′ is a function of α.

(Enter q(alpha) for the quantile qα(N(0,1)) of the normal distribution.)

qα(χ21)=

Answer 1

Answer is [q(alpha/2)]²

The detailed solution is given in the pictures below.

Please go through them carefully specially the notations.

Hope the solution helps. Thank you.

(Please do comment if further help is required)

[q_(alpha/2) N(0,1) ]^2 is the required answer for the question asked.