Abstract. This paper begins by defining the basic aspects of probability, including the probability space and random variables. We explore the types and qualities of random variables, as well as di↵erent distributions and their properties, with the goal of building the Poisson Process, and finally the Compound Poisson Process. This is an important counting process that can be applied to many in...

This article employs the relation between probabilities of two consecutive values a Poisson random variable to derive conditions for weak convergence point processes process. As applications, we consider starting points k -runs in sequence Bernoulli variables, constructed using inradii and circumscribed radii inhomogeneous Poisson–Voronoi tessellations large nearest neighbor distances Boolean m...