Remarks on the independence of the sample mean and sample variance from a normal population

Document Type

Article

Publication Date

1-1-1990

Abstract

Many statistics texts prove that (formula presented) and S2 are stochastically independent by showing that the moment generating function of nS2/σ2, given (formula presented)= (formula presented), is independent of (formula presented). A key step involves showing that a complicated n-dimensional integral is equal to one. We accomplish this directly by using the Lagrange reduction procedure on the integrand, followed by a change of variables using a non-singular linear transformation with Jacobian equal to one. The transformed integral, when viewed in iterated form splits into a product of well-known integrals. © 1990 Taylor and Francis Group, LLC.

Identifier

84946360248 (Scopus)

Publication Title

International Journal of Mathematical Education in Science and Technology

External Full Text Location

https://doi.org/10.1080/0020739900210411

e-ISSN

14645211

ISSN

0020739X

First Page

585

Last Page

587

Issue

4

Volume

21

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