Award Date

5-1-2013

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Rohan Dalpatadu

Second Committee Member

Gennady Bachman

Third Committee Member

Amei Amei

Fourth Committee Member

Ashok Singh

Fifth Committee Member

Pushkin Kachroo

Number of Pages

38

Abstract

The Negative Hypergeometric distribution represents waiting times when drawing from a finite sample without replacement. It is analogous to the negative binomial, which models the distribution of waiting times when drawing with replacement. Even though the Negative Hypergeometric has applications it is typically omitted from textbooks on probability and statistics and is not generally known. The main purpose of this thesis is to derive expressions for the mean and variance of a new application of the Negative Hypergeometric to gaming and gambling. Other applications are described as well.

Keywords

Bonus games; Compound distributions; Discrete probability; Gambling; Hypergeometric distribution; Hypergeometric functions; Mixture distributions (Probability theory); Slot machines; Urn models; Wheel of Fortune

Disciplines

Applied Mathematics | Probability | Statistics and Probability

Language

English


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