A RAPID REVIEW OF PROPERTIES OF POISSON PROBABILITY DISTRIBUTION AND ITS VERIFICATION WITH AN REAL LIFE EXAMPLE

The Poisson distribution, a cornerstone of probability theory, is instrumental in modeling the occurrence of rare events over a fixed interval of time or space. This study delves into the mathematical properties of the Poisson distribution, elucidating its derivation from the binomial distribution and highlighting key characteristics such as its mean, variance, and moment generating function. The research underscores the distribution's defining feature: the mean being equal to the variance, an attribute that simplifies its application across diverse fields. Real-life applications are explored extensively to demonstrate the utility of the Poisson distribution in various domains.