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If you are given a sample of size $n$, and you don't know the mean of the underlying distribution, then you should use the version of estimated variance with $n-1$. This slick trick (replacing $n$ with $n-1$ when computing estimated variance) makes the empirical estimator of variance what is called "unbiased", meaning that the expected value of the variance ...


I think you need to check your calculations. For example, I get $E(Z) =6.15$, but I haven't checked $E(Z^2)$ yet. Would it be cheating to chuck this into an excel spreadsheet?

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