Introduction to Exact Sampling Distribution

This distribution was first described by the German statistician Friedrich Robert Helmert in papers of 1875, where he computed the sampling distribution of the sample variance of a normal population. The distribution was independently rediscovered by the English mathematician Karl Pearson in the context of goodness of fit, for which he developed his Pearson's chi-squared test and computed table of values. The name "chi-squared" ultimately derives from Pearson's shorthand for the exponent in a multivariate normal distribution with the Greek letter Chi. The idea of a family of "chi-squared distributions", however, is not due to Pearson but arose as a further development due to Fisher in the 1920 The square of a standard normal variate is known as a chi-square (read as Ki) variate with 1 degree of freedom (d.f.) A chi-squared variable with n degrees of freedom is defined as the sum of the squares of n independent standard normal random variables.