Proving Variance of t Distribution

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SUMMARY

The variance of the t distribution is defined as the second moment of its probability density function (pdf) for degrees of freedom (n) greater than 2. For n equal to 1 or 2, the variance is undefined. The derivation of the variance for n greater than 2 utilizes Wallis integrals, as discussed in the referenced Tutorial 2. This foundational understanding is crucial for statistical analysis involving the t distribution.

PREREQUISITES
  • Understanding of probability density functions (pdf)
  • Familiarity with statistical moments
  • Knowledge of Wallis integrals
  • Basic concepts of the t distribution
NEXT STEPS
  • Study Wallis integrals in detail
  • Learn about the properties of the t distribution
  • Explore the derivation of statistical moments
  • Review applications of the t distribution in hypothesis testing
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Statisticians, data analysts, and researchers involved in statistical modeling and hypothesis testing will benefit from this discussion on the variance of the t distribution.

DavidLiew
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How to prove the variance of the t distribution?
 
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DavidLiew said:
How to prove the variance of the t distribution?

I'm not sure "proof" is the proper concept here since the variance of the t distribution is defined as the second moment of the pdf as for all distributions. The variance is not defined for n=1,2. For values of n>2 the variance is derived from Wallis integrals discussed here in Tutorial 2:

http://www.aiaccess.net/English/Glossaries/GlosMod/e_gm_t_distri.htm#Tut_2_Variance

http://129.81.170.14/~vhm/papers_html/wrsf.pdf
 
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