Independence of the Sample Mean and Variance for Normal Distributions : A Proof by Induction
Year: 2015
Type: article
Abstract: It is well known that the sample mean and variance of a random sample drawn from a normal population independently follow normal and chi-squared distributions. The proof for the independence usually relies on the condition for the independence of two quadratic forms or a linear and a quadratic form, the orthogonal transformation, or the concept of sufficiency. This note gives a much more straightforward proof by induction without using such advanced subjects.
Author: Masayuki Hirukawa
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W625882338