The collector's problem with group drawings
Wolfgang Stadje · Advances in Applied Probability · 1990
We consider sampling with replacement of equiprobable groups of a fixed sizemfrom a finite populationS.Given a subsetA⊂S, the distributions of (a) the number of distinct elements ofAin a sample of sizekand (b) the sample size necessary to obtain at least saynelements ofAare given. Neat formulas are given especially for the expected values of these, as well as of some related random variables. Further we derive an optimal strategy to collect all elements ofSunder the assumptions that sampling one group costsαmonetary units and that it is possible to purchase the elements which are missing at the end of the sampling procedure at a price ofβ>α/mper element.