Degree Name

MS (Master of Science)


Mathematical Sciences

Date of Award


Committee Chair or Co-Chairs

Anant Godbole

Committee Members

Michele Joyner, JeanMarie Hendrickson


What is the probability that in a fair coin toss game (a simple random walk) we go bankrupt in n steps when there is an initial lead of some known or unknown quantity $m? What is the distribution of the number of steps N that it takes for the lead to vanish? This thesis explores some of the features of this first passage to the origin (FPO) distribution. First, we explore the distribution of N when m is known. Next, we compute the maximum likelihood estimators of m for a fixed n and also the posterior distribution of m when we are given that m follows some known prior distribution.

Document Type

Thesis - unrestricted


Copyright by the authors.

Included in

Analysis Commons