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In group‐testing, a set of x units is taken from a total starting set of N units, and the x units (1 ≦ x ≦ N) are tested simultaneously as a group with one of two possible outcomes: either all x units are good or at least one defective unit is present (we don't know how many or which ones). Under this type of testing, the problem is to find the best integer x for the first test and to find a rule for choosing the best subsequent test‐groups (which may depend on results already observed), in order to minimize the expected total number of group‐tests required to classify each of the N units as good or defective. It is assumed that the N units can be treated like independent binomial chance variables with a common, known probability p of any one being defective; the case of unknown p and several generalizations of the problem are also considered.

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Formulae are presented for the variance and higher moments of the present value of single-stage rewards in a finite Markov decision process. Similar formulae are exhibited for a semi-Markov decision process. There is a short discussion of the obstacles to using the variance formula in algorithms to maximize the mean minus a multiple of the standard deviation.

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