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On the number of games played in a best of (2 n – 1) series
Author(s) -
Nagariaja H. N.,
Chan W. T.
Publication year - 1989
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198906)36:3<297::aid-nav3220360307>3.0.co;2-w
Subject(s) - series (stratigraphy) , mathematics , estimator , variance (accounting) , distribution (mathematics) , combinatorics , discrete mathematics , statistics , mathematical analysis , accounting , business , biology , paleontology
Let p (⩾0.5) denote the probability that team A beats B in a single game. The series continues until either A or B wins n games. Assuming that these games are independent replications, we study some features of the distribution of X n , the number of games played in the series. It is shown that X n is unimodal, has an IFRA distribution, and is stochastically decreasing in p . Close approximations to its mode, mean, and variance are given. Finally, it is shown that the maximum‐likelihood estimator of p based on X n is unique.