Çibuku, Denajda
(2019)
*A NOTE ON AN ALTERNATIVE FORMULA FOR CALCULATING S2 AND ITS USES.*
Journal of Natural Sciences and Mathematics of UT, 4 (7-8).
pp. 158-163.
ISSN 2671-3039

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## Abstract

This article is referred to the article of Stigler. That gives the proof of the joint distribution between the sample mean and the sample variance with the assumption that the population is normally. The machine formula of S^2 has been used during the proof by Stigler, the bivariate distribution is being needed and also the Induction Theory. Starting in this context and as part of statistical education, it has been brought a different viewpoint of doing the proofs of some important results and derivations of the sample mean distribution. It has been changed the scheme of proof replaying the machine formula with an alternative formula of S^2, which is a less used definition of the sample variance. Compared with Stigler this method of proof gives less calculation. It is of interest to know what the covariance of the sample mean and the sample variance is without the assumption of normality. One method of proof is being done by Zhang (2007). He did not use the well-known formula of the sample variance, but it has been used the alternative formula to give the same result in an easer way. It, also, has been used the fact that the third moment of the sample population exists. The computations were straightforward and did not require advanced mathematical notions. Is been showed an example of Poisson distributed to illustrate the fact that the covariance of the joint distribution of the sample variance and the sample mean were zero, but they were not independent. It has been constructed a table of joint probability and from this has been displayed the result. Starting from this example and regarding challenges in teaching Statistics we pretend in the future to apply the distribution of an average of Poisson random variables in advance Statistics.

Item Type: | Article |
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Subjects: | Q Science > Q Science (General) |

Divisions: | Faculty of Engineering, Science and Mathematics > School of Mathematics |

Depositing User: | Unnamed user with email zshi@unite.edu.mk |

Date Deposited: | 22 Feb 2020 18:40 |

Last Modified: | 22 Feb 2020 18:40 |

URI: | http://eprints.unite.edu.mk/id/eprint/449 |

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