11.2: Facts About the Chi-Square Distribution
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The notation for the chi-square distribution is:
\[\chi \sim \chi_{d f}^{2}\nonumber\]
where \(df\) = degrees of freedom which depends on how chi-square is being used. (If you want to practice calculating chi-square probabilities then use \(df = n - 1\). The degrees of freedom for the three major uses are each calculated differently.)
For the \(\chi^2\) distribution, the population mean is \(\mu = df\) and the population standard deviation is \(\sigma=\sqrt{2(d f)}\).
The random variable is shown as \(\chi^2\).
The random variable for a chi-square distribution with \(k\) degrees of freedom is the sum of \(k\) independent, squared standard normal variables.
\[\chi^{2}=\left(Z_{1}\right)^{2}+\left(Z_{2}\right)^{2}+\ldots+\left(Z_{k}\right)^{2}\nonumber\]