Why the chi-square distribution is positively skewed

Chi-square distribution

continuous probability distribution (distribution) introduced as a test distribution by Helmert (1876) and Pearson (1900). Are n random variables X1, ..., Xn stochastically independent and each with standard normal distribution (standard normal distribution), then is the sum of the squares of these random variables-distributed with n degrees of freedom. The chi-square distribution has one parameter, the number n of degrees of freedom. It is unicodular and strongly left-hand part for small n (skewness).

The density function of a chi-square distribution with n degrees of freedom is given by

The associated expected value is given by n and the variance is given by 2n. The chi-square distribution is a special gamma distribution. There are tables for quantiles of -Distribution. For large n, the distribution function can be approximated using the normal distribution. The chi-square distribution is used, for example, in statistical tests for variances in normal distributions and in the chi-square test.