Elemental r bewijs van de onafhankelijkheid van gemiddelde en spreiding bij steekproeven uit een normale verdeling

J. van IJzeren

Statistica Neerlandica, 1952, vol. 6, issue 2, 113-119

Abstract: 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 mn and the “deviation” xn–mn–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 xi–mi‐1(i = 2, 3, …, n), which are completely independent and represent the n–1 degrees of freedom in s.

Date: 1952
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