# zbMATH — the first resource for mathematics

On the distribution of the number of successes in independent trials. (English) Zbl 0073.13902
A sequence of independent trials being given, where the probability $$p_j$$ of the event $$A$$ varies with the rank $$j$$ of the trial, the author examines the problem of the maximum and the minimum of the mathematical expectation of a function of the frequency $$S$$ of this event, when $$p_j$$ verifies the conditions $$0\leq p_j\leq 1$$, $$\sum_{j=1}^n p_j= np$$, $$p$$ being given. The results are enunciated with very great precision in the geometrical language adopted by the author. In these enunciations the conditions of equality among all $$p_j$$ or of some of them, are playing an important role. The theorems obtained, can be used in some estimation-problems.
Reviewer: O. Onicescu

##### MSC:
 6.2e+16 Exact distribution theory in statistics 6e+06 Probability distributions: general theory
Statistics
Full Text: