Chi-square distribution
A sum of the squares of $k$ independent standard normal random variables
$$
Z_1^2 + Z_2^2 + \cdots + Z_k^2 \;\sim\; \chi^2(k)
$$
$$
f(x) =
\begin{cases}
\frac{x^{\frac{k}{2}-1}e^{-\frac{x}{2}}}{2^{\frac{k}{2}}\Gamma\big(\frac{k}{2}\big)}, & \text{if $x > 0$,} \\
0, & \text{otherwise.}
\end{cases}
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\text{where $k$ is the degree of freedom (the number of the squares)} \\
\\
\text{and $\Gamma\bigg(\frac{k}{2}\bigg)$ is the gamma function.}
$$