Geodesic
A note on correlation coefficient between random events
Discussiones Mathematicae. Probability and Statistics, Tome 35 (2015) no. 1-2, pp. 57-60
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Correlation coefficient is a well known measure of (linear) dependence between random variables. In his textbook published in 1980 L.T. Kubik introduced an analogue of such measure for random events A and B and studied its basic properties. We reveal that this measure reduces to the usual correlation coefficient between the indicator functions of A and B. In consequence the resuts by Kubik are obtained and strenghted directly. This is essential because the textbook is recommended by many universities in Poland.
Keywords: correlation coefficient between random events, correlation coefficient for random variables, synergy phenomenon 
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Stępniak, Czesław. A note on correlation coefficient between random events. Discussiones Mathematicae. Probability and Statistics, Tome 35 (2015) no. 1-2, pp. 57-60. http://geodesic.mathdoc.fr/item/DMPS_2015_35_1-2_a3/

[1] P. Brémaud, An Introduction to Probabilistic Modeling (Springer-Verlag, New York, 1994).

[2] L.T. Kubik, Probability. A Textbook for Teaching Mathematics Studies (in Polish) 9Polish Scientific Publishers, Warsaw, 1980).

[3] K. Maciąg and C. Stępniak, Lack of synergy regression models, Comm. Statist. Theory Methods 43 (2014), 383-391.

[4] D. Stirzaker, Elementary Probability (Cambridge Univ. Press, Cambridge, 1994).