**Process** A random variable that arrises as the sum of the square of $n$ normally distributed variables follows a chi squared distribution with $n$ degrees of freedom.
If $y = x_1^2 + x_2^2 + \dots + x_n^2$ when $x_i \sim \operatorname{N}(0,1); i = 1 \dots n$ then
$y \sim \chi^2_n$ with $n$ degrees of freedom
$
E(\chi^2_n) = n
$
**Typical use** While the [[sample mean]] is usually either normally distributed or follows a t-distribution, the [[sample variance]]7 [[]]when the population mean is know follows a Chi-Squared distribution.
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- Links: [[Student-T distribution]] [[Sampling Distributions]] [[MIT 2.830J Control of Manufacturing Processes - Lec 6]]
- Created at: [[2021-11-25]]