# The chi-square distribution

The chi-square statistics are defined by the following formula:

Here, *n* is the size of the sample, *s* is the standard deviation of the sample, and *σ* is the standard deviation of the population.

If we repeatedly take samples and define the chi-square statistics, then we can form a chi-square distribution, which is defined by the following probability density function:

Here, *Y*_{0} is a constant that depends on the number of degrees of freedom, *Χ*_{2} is the chi-square statistic, *v = n - 1* is the number of degrees of freedom, and *e*

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