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The Chi-Squared Distribution

​
parameter ν
4
mean:
ν
=
4
variance:
2ν
=
8
moment generating function:
-ν/2
(1-2t)
=
1
2
(1-2t)
The sum of
ν
squares of independent standard normal random variables is a chi-squared random variable with
ν
degrees of freedom. This distribution is a special case of the gamma distribution that arises in statistics when estimating the variance of a population. The red vertical line marks the mean of the distribution.
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