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For any positive integer <math>k</math>, the chisquare distribution with k degrees of freedom is the probability distribution of the random variable
The chisquare distribution has numerous applications in inferential statistics, for instance in chisquare tests and in estimating variances. It enters the problem of estimating the mean of a normally distributed population and the problem of estimating the slope of a regression line via its role in Student's tdistribution. It enters all analysis of variance problems via its role in the Fdistribution[?], which is the distribution of the ratio of two chisquared random variables.
Its probability density function is
The expected value of a random variable having chisquare distribution with k degrees of freedom is k and the variance is 2k. Note that 2 degrees of freedom leads to an exponential distribution.
The chisquare distribution is a special case of the gamma distribution.
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