What This Document Is
This document contains a collection of worked examples designed to accompany Lecture 05 of MATH 370X, Actuarial Problem Solving at the University of Illinois at Urbana-Champaign. It focuses on the practical application of discrete probability distributions, a core component of actuarial science. These examples build upon the theoretical foundations presented in the lecture and demonstrate how to translate concepts into concrete calculations. It’s intended as a supplementary resource to reinforce understanding and build problem-solving skills.
Why This Document Matters
Students enrolled in MATH 370X – or those studying similar actuarial science or probability courses – will find this resource particularly valuable. It’s best utilized *after* attending the corresponding lecture to solidify comprehension and practice applying the techniques discussed. Aspiring actuaries will benefit from working through these examples, as they mirror the types of problems encountered in professional exams and real-world actuarial work. This material is ideal for self-study, homework assistance, and exam preparation.
Topics Covered
* Discrete Random Variables
* Probability Functions
* Moment Generating Functions
* Expected Value and Variance Calculations
* Poisson Distribution Applications
* Geometric Distribution Applications
* Hypergeometric Distribution Applications
* Probability Calculations with Independent Events
What This Document Provides
* A series of illustrative examples related to frequently used discrete distributions.
* Problems designed to test understanding of key concepts.
* Scenarios involving real-world applications of discrete probability.
* Opportunities to practice applying formulas and techniques discussed in lecture.
* A foundation for tackling more complex actuarial problems.
