= Coupon collector waiting-time variance
{title2=$\operatorname{Var}(T)=n^2\sum_{r=1}^nr^{-2}-n\sum_{r=1}^nr^{-1}$}
For uniform independent draws of $n$ coupon types, the waiting times with $r$ unseen types remaining are independent positive-support <geometric distributions> of parameter $r/n$. Summing their means gives $n\sum_{r=1}^n1/r$, and summing their variances gives the displayed formula. <Independence> follows from fresh draws after each discovery and the fact that the next stage's conditional distribution depends only on the count of remaining types.
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