What This Document Is
This handout provides focused instruction on frequently used continuous probability distributions, a core component of actuarial problem solving. It’s designed to supplement lectures from MATH 370X at the University of Illinois at Urbana-Champaign, offering a concentrated review of key concepts and techniques. The material builds upon foundational knowledge of probability and prepares students for more advanced applications within actuarial science.
Why This Document Matters
This resource is invaluable for students currently enrolled in an actuarial problem-solving course, or those preparing for actuarial exams. It’s particularly helpful when you need a concise reference guide to understand the characteristics and applications of various continuous distributions. Students will find it useful during independent study, when working through practice problems, or as a refresher before assessments. Access to the full content will allow you to confidently apply these distributions to real-world actuarial scenarios.
Topics Covered
* Uniform Distribution – understanding its properties and distinctions from discrete counterparts.
* Normal Distribution – exploring its characteristics, including the impact of variance and standardization.
* Exponential Distribution – examining its use in modeling time-to-event scenarios and its relationship to the Poisson distribution.
* Gamma Distribution – investigating its properties and connection to the exponential distribution.
* Normal Approximation – learning how to approximate discrete distributions using the normal distribution, including correction factors.
* Linear Combinations of Normal Random Variables – understanding how to work with combinations of normally distributed variables.
What This Document Provides
* A focused overview of key continuous probability distributions.
* Guidance on transforming variables for probability calculations.
* Discussion of the relationship between different distributions.
* Information on applying the normal approximation to discrete distributions.
* A standard normal distribution table for probability lookups (table itself is included).
* Definitions of important mathematical functions used in the context of probability.
