ABSTRACT
Asymptotic distribution theory is the study of the properties of infinite sequences of random variables. One of the most important features of convergence in distribution is the ability to identify useful rules and an occasional shortcut for the computation of some probabilities. The Poisson distribution assigns probability for all non-negative integers. One of the most fascinating observations in probability is the finding that so many random variables appear to follow a normal distribution. Some random variables can be transformed into new random variables that follow a normal distribution. The use of the normal distribution as an approximation to the distribution of other distributions will begin with an examination of the manner in which the Poisson distribution produces probabilities that are approximately Gaussian. The demonstration that a binomial distribution could be usefully approximated by the normal distribution was first proved by De'Moivre and Laplace. Asymptotic distribution is central to the study of the properties of infinite sequences of random variables.
