Premium
Elemental r bewijs van de onafhankelijkheid van gemiddelde en spreiding bij steekproeven uit een normale verdeling
Author(s) -
IJzeren J.
Publication year - 1952
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1952.tb00986.x
Subject(s) - mathematics , independence (probability theory) , combinatorics , standard deviation , sample mean and sample covariance , distribution (mathematics) , statistics , mathematical analysis , estimator
Summary Elementary proof of the independence of mean and variance of samples from a normal distribution. Usually the independence of mean and variance of samples from a normal distribution is proven by some n‐dimensional reasoning. The present article starts by proving the independence of the sample‐mean m n and the “deviation” x n –m n –1 of the last sampled element from the previous sample‐mean. This result gives an easy approach to the independence theorem, which is proven by a step‐by‐step process. A more elaborate version of the proof reveals the nature of the s‐distribution. Use is made of the n–i deviations x i –m i‐1 (i = 2, 3, …, n), which are completely independent and represent the n–1 degrees of freedom in s.