How can I find the expected value and median of $X\sim \chi^2$ with degrees of freedom of $12\,$? The information I get from every other source, I find, is confusing. I am using R.


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The mean of a $\chi^2$ random variable is equal to the degrees of freedom. The median has no close form afaik, you can get it in R from the inverse cumulative distribution function (aka the quantile function) evaluated at $0.5$:

qchisq(0.5, dof)

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