MS (Master of Science)
Date of Award
Committee Chair or Co-Chairs
Nicole Lewis, JeanMarie Hendrickson
A probability distribution is a statistical function that describes the probability of possible outcomes in an experiment or occurrence. There are many different probability distributions that give the probability of an event happening, given some sample size n. An important question in statistics is to determine the distribution of the sum of independent random variables when the sample size n is fixed. For example, it is known that the sum of n independent Bernoulli random variables with success probability p is a Binomial distribution with parameters n and p: However, this is not true when the sample size is not fixed but a random variable. The goal of this thesis is to determine the distribution of the sum of independent random variables when the sample size is randomly distributed as a Poisson distribution. We will also discuss the mean and the variance of this unconditional distribution.
Thesis - Open Access
Pfister, Mark, "Distribution of a Sum of Random Variables when the Sample Size is a Poisson Distribution" (2018). Electronic Theses and Dissertations. Paper 3459. https://dc.etsu.edu/etd/3459
Copyright by the authors.