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

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.