×

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:
62E15 Exact distribution theory in statistics
60E05 Probability distributions: general theory
Keywords:
Statistics
PDF BibTeX XML Cite
Full Text: DOI