Question: Approximation of chi-square quantiles. For 0 < < 1 and n 2 N, let 2 nI be the -quantile of the 2 n-distribution and

Approximation of chi-square quantiles. For 0 < ˛ < 1 and n 2 N, let 2 nI˛ be the

˛-quantile of the 2 n-distribution and ˆ1.˛/ the ˛-quantile of the standard normal distribution.

Show that .2 nI˛

n/=

p 2n ! ˆ1.˛/ as n ! 1. Hint: Use Problem 4.17 or Example (7.27b).

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