The Student t-distribution

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stochastikclips

Published on Dec 20, 2022
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The t-distribution is named after William Sealy Gosset (1876--1937), who published under the pseudonym Student. Gosset discovered the t-distribution in 1908; however, it was known to Jacob Lüroth much earlier. The t-distribution is a distribution derived from the normal distribution, which in particular provides confidence intervals for the unknown expected value of a normal distribution with unknown variance and provides critical values ​​for the so-called t-test. This video shows the problem from which the t-distribution arises, and the t-distribution with k degrees of freedom is derived as the distribution of a quotient of stochastically independent random variables, where the numerator is standard normally distributed and the denominator is distributed like the root of a reduced chi-square distribution with k degrees of freedom. The density of the t-distribution is derived in the video using the quotient rule for densities, see • The quotient rule for densities For this video, it is helpful to know results about the multivariate normal distribution.

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