On degenerate Poisson random variable

In this paper, we delve into the intricate properties of degenerate Poisson random variables, exploring their moment generating function, the law of large numbers, and the central limit theorem. Our study into the law of large numbers unveils the convergence patterns of degenerate Poisson random variables, enlightening the stability and predictability of their expected values and variances. Further enriching our study, we extend our focus to the central limit theorem, unravelling the interesting results that emerge as the sample size approaches infinity.