A note on the sample covariance from a bivariate normal population

Anwar H Joarder; M Hafidz Omar

doi:10.3329/jsr.v59i1.83688

A note on the sample covariance from a bivariate normal population

Authors

Anwar H Joarder Department of Computer Science and Engineering Northern University of Business and Technology Khulna, Khulna 9100, Bangladesh
M Hafidz Omar Department of Mathematics and Statistics King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.

DOI:

https://doi.org/10.3329/jsr.v59i1.83688

Keywords:

Sample covariance, bivariate normal distribution, correlated chisquare variables, moment generating function

Abstract

Both the Moment Generating Function and the Probability Density Function of sample covariance based on a bivariate normal distribution have been presented in a simpler way by using conditional distributions. We also prove that the random variable sample covariance is a linear combination of two chi-square random variables if they are statistically independent.

Journal of Statistical Research 2025, Vol. 59, No. 1, pp. 99-106

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Published

2025-08-19

How to Cite

Joarder, A. H., & Omar, M. H. (2025). A note on the sample covariance from a bivariate normal population. Journal of Statistical Research , 59(1), 99–106. https://doi.org/10.3329/jsr.v59i1.83688