#### Degree Name

MS (Master of Science)

#### Program

Mathematical Sciences

#### Date of Award

8-2018

#### Committee Chair or Co-Chairs

Robert Price

#### Committee Members

Nicole Lewis, JeanMarie Hendrickson

#### Abstract

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.

#### Document Type

Thesis - unrestricted

#### Recommended Citation

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

Copyright by the authors.