Date of Completion
Spring 5-17-2024
Thesis Advisor(s)
Iddo Ben-Ari
Honors Major
Mathematics
Disciplines
Mathematics | Probability | Statistics and Probability
Abstract
A sequence of random variables (RVs) is exchangeable if its distribution is invariant under permutations. For example, every sequence of independent and identically distributed (IID) RVs is exchangeable. The main result on exchangeable sequences of random variables is de Finetti's theorem, which identifies exchangeable sequences as conditionally IID. In this thesis, we explore exchangeability, provide an elementary proof of de Finetti's theorem, and present two applications: the classical Polya's urn model and a toy model for biological evolution.
Recommended Citation
Haddad, Renee, "Exchangeability and a Model of Biological Evolution" (2024). Honors Scholar Theses. 988.
https://digitalcommons.lib.uconn.edu/srhonors_theses/988