Category:Chi-Squared Distribution

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This category contains results about the chi-squared distribution.
Definitions specific to this category can be found in Definitions/Chi-Squared Distribution.

Let $r$ be a strictly positive integer.

Let $X_1, X_2, \ldots, X_r$ be $r$ pairwise independent continuous random variables each with a standard Gaussian distribution.

Let $X := \ds \sum_{i \mathop = 1}^r {X_i}^2$ be the sum of the squares of $X_1, X_2, \ldots, X_r$.


Then $X$ is said to have a chi-squared distribution with $r$ degrees of freedom.


This is written:

$X \sim \chi_r^2$

where $\chi$ is the Greek letter $\chi$ (chi).