Related to chi-squared functions

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I'm finding difficulty in finding what type of function it is in continuous distributions in probability. Mainly how can I identify whether a function is chi-squared or not?

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A $\chi^2$ is simply a particular probability density function (see wikipedia)

You can prove that the sum of the square of normal independent variables follows a $\chi ^2$, which explains why it is used so often to do statistical tests on variance. There is not much more to it than that.