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By: Neil
E. Cotter
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Statistics
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Student's or t-distribution |
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Distribution of sample variance |
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Tool: For n independent samples, Xi, from a normal (or gaussian) distribution with mean m and variance s2, the probability density function of the normalized sample variance,
(where n = n – 1,
, and 
)
has a chi‑squared distribution with n degrees of freedom:
or
Proof: See derivation of χ2 distribution | (pdf).
Ref: Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, and Keying Ye, Probability and Statistics for Engineers and Scientists, 8th Ed., Upper Saddle River, NJ: Prentice Hall, 2007.