What This Document Is
This document contains a collection of worked examples designed to accompany Lecture 04 of MATH 370X, Actuarial Problem Solving at the University of Illinois at Urbana-Champaign. It focuses on applying theoretical concepts related to probability distributions and expectation to a variety of practical scenarios. These examples serve as a crucial bridge between the lecture material and independent problem-solving. The document is dated October 3, 2016, and appears to be a supplemental resource created by the instructor, Saumil Padhya.
Why This Document Matters
This resource is invaluable for students enrolled in MATH 370X who are looking to solidify their understanding of expectation, distribution parameters, and related calculations. It’s particularly helpful when you’re ready to move beyond the foundational concepts presented in lecture and begin tackling more complex problems. Working through these examples will build confidence and improve your ability to apply actuarial principles. It’s best used *after* attending the corresponding lecture and reviewing relevant textbook sections, as a means of active learning and self-assessment.
Topics Covered
* Discrete and Continuous Random Variables
* Probability Distributions and Functions (PDFs & CDFs)
* Expected Value (Mean) and Variance Calculations
* Moment Generating Functions (MGFs)
* Percentiles and Conditional Distributions
* Applications to Insurance Claim Analysis
* Geometric Distributions
What This Document Provides
* A series of illustrative examples covering a range of problem types.
* Problems involving finding expected values in different contexts.
* Exercises focused on calculating mean and variance for various distributions.
* Applications of moment generating functions to determine moments and variance.
* Problems related to determining percentiles of distributions.
* A practical example involving claim size distributions in auto insurance.
* Problems designed to test understanding of discrete, non-negative integer-valued random variables.
