An Integral Proof of the Joint M.G.F. of Sample Mean and Variance

Anwar H Joarder; A Laradji

doi:10.3329/ijss.v24i20.78211

An Integral Proof of the Joint M.G.F. of Sample Mean and Variance

Authors

Anwar H Joarder Department of Mathematics, School of Science and Engineering, Al Akhawayn University in Ifrane, Ifrane 53000, Morocco
A Laradji Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

DOI:

https://doi.org/10.3329/ijss.v24i20.78211

Keywords:

Sample mean, sample variance, t-Test, independence, moment generating function

Abstract

Without assuming independence of sample mean and variance, or without using any conditional distribution, we present an integral proof of the joint moment generating function for sample mean and variance for independently, identically and normally distributed random variables. This proves the independence of sample mean and variance which is the basis of Student t-Test and many other inferential methods.

IJSS, Vol. 24(2)s (Special Issue), December, 2024, pp 19-23

Abstract
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Published

2024-12-23

How to Cite

Joarder, A. H., & Laradji, A. (2024). An Integral Proof of the Joint M.G.F. of Sample Mean and Variance. International Journal of Statistical Sciences , 24(20), 19–23. https://doi.org/10.3329/ijss.v24i20.78211