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

J. IJzeren, van

    Research output: Contribution to journalArticleAcademicpeer-review

    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.
    Original languageEnglish
    Pages (from-to)113-119
    Number of pages7
    JournalStatistica Neerlandica
    Volume6
    Issue number2
    DOIs
    Publication statusPublished - 1952

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