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## Main Question or Discussion Point

Hi all,

I am trying to understand two things from a paper

The ratio of a standard normal by the square root of a a chi squared divided by its df ( degrees of freedom) is a t distribution. So

1) What is the dist of square root of Chi squared? I know a normal squared is a chi squared, but a chi squared may not necessarily come about ad the square of a normal

2) Why does the ratio of a standard normal by the square root of a chi squared a t distribution? What result is this?

Only somewhat related result can think of is that ratio of independent standard normals ( of course, nonzero denominator) is a Cauchy. Edit: I wanted to double check the claim that the square root of a chi squared is a chi squared because this does not seem true about the square root of a square normal, which seems should be normal.

Thanks.

I am trying to understand two things from a paper

The ratio of a standard normal by the square root of a a chi squared divided by its df ( degrees of freedom) is a t distribution. So

1) What is the dist of square root of Chi squared? I know a normal squared is a chi squared, but a chi squared may not necessarily come about ad the square of a normal

2) Why does the ratio of a standard normal by the square root of a chi squared a t distribution? What result is this?

Only somewhat related result can think of is that ratio of independent standard normals ( of course, nonzero denominator) is a Cauchy. Edit: I wanted to double check the claim that the square root of a chi squared is a chi squared because this does not seem true about the square root of a square normal, which seems should be normal.

Thanks.

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