Dimorphic properties of Bernoulli random variable

Author:

Kim Taekyun1,Kim Dae2,LeeaHyunseok L1,Park Seong-Ho1

Affiliation:

1. Department of Mathematics, Kwangwoon University, Seoul, Republic of Korea

2. Department of Mathematics, Sogang University, Seoul, Republic of Korea

Abstract

The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two expressions on sums of products of degenerate Stirling numbers of the second kind and Stirling numbers of the first kind connected with those two different sums of identically independent Bernoulli random variables.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference18 articles.

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2. Aizenman, M.; Germinet, F.; Klein, A.; Warzel, S. On Bernoulli decompositions for random variables, concentration bounds, and spectral localization, Probab. Theory Related Fields 143 (2009), no. 1-2, 219-238.

3. Araci, A. A new class of Bernoulli polynomials attached to polyexponential functions and related identities, Adv. Stud. Contemp. Math. (Kyungshang) 31 (2021), no. 2, 195-204.

4. Comtet, L. Nombres de Stirling generaux et fonctions symetriques, C. R. Acad. Sci. Paris. (Series A), 275 (1972), 747-750.

5. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. II., 2nd ed. John Wiley & Sons, Inc., New York-London- Sydney, 1971.

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