Submitted:
14 November 2019
Posted:
15 November 2019
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Abstract
In this paper, we introduce two discrete degenerate random variables, namely the degenerate binomial and degenerate Poisson random variables. We deduce the expectations of the degenerate binomial random variables. We compute the generating function of the moments of the degenerate Poisson random variables, which leads us to define the new type degenerate Bell polynomials, and hence obtain explicit expressions for the moments of those random variables in terms of such polynomials. We also get the variances of the degenerate Poisson random variables. Finally, we illustrate two examples of the degenerate Poisson random variables.
Keywords:
discrete degenerate random variables
; degenerate binomial random variable
; degenerate Poisson random variable
; new type degenerate Bell polynomials
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