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What remarks about the tails can we infer from the density function of $X^n$ if $X$ is standard normally distributed

Mathematics Asked by Hoang Skadi on January 17, 2021

  1. Find the pdf of $X^n$ if $Xsim N(0,1)$

Is there any general formula for this or we have to divide into 2 cases: $n$ is an odd number; and $n$ is an even number?

  1. What can we learn about the tails of the densities when $n$ receives different values?

I hope to find some help. Thank you.

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