Chi-Squared distribution¶
Chi squared is related to the distribution of the sample variance, and can be used to estimate the true variance of the distribution.
\[
S \sim X^2_v
\]
Moments¶
Mean¶
\[E[S] = v\]
Variiance¶
\[Var(S) = 2v\]
Connection to Gaussian¶
A Chi-Square with \(v\) degrees of freedom can be defined as a sum of \(v\) standard normals.
\[\begin{split} S \sim X^2_v \\ S = \sum_{i=1}^{v} Z_i^2 \\ Z_i \sim N(0,1)\end{split}\]