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MATH 471 Syllabus

Problem Solving for Actuarial Exam P

Revised: January 7, 2020

Course Description

Advanced problem solving by means of extensive review and practice.  Preparing students for Exam P of the Society of Actuaries and the Casualty Actuarial Society.

Prerequisite: MATH 370

Corequisite: MATH 256

Student Learning Objectives

From the 鈥渓earning objectives鈥� listed for this professional exam, candidates (students) should be able to use and apply the following concepts in a risk management context:

  1. General Probability (Set functions including set notation and basic elements of probability, Mutually exclusive events, Addition and multiplication rules, Independence of events, Combinatorial probability, Conditional probability, Bayes Theorem/Law of total probability)
  2. Univariate probability distributions (including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, gamma, and normal), Probability functions and probability density functions, Cumulative distribution functions, Mode, median, percentiles, and moments, Variance and measures of dispersion, Moment generating functions, Transformations.
  3. Multivariate probability distributions (including the bivariate normal), Joint probability functions and joint probability density functions, Joint cumulative distribution functions, Central Limit Theorem, Conditional and marginal probability distributions, Moments for joint, conditional, and marginal probability distributions, Joint moment generating functions, Variance and measures of dispersion for conditional and marginal probability distributions, Covariance and correlation coefficients, Transformations and order statistics, Probabilities and moments for linear combinations of independent random variables

Text

Weishaus, Abraham. ASM Study Manual for Exam P, 2nd edition.

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline

  1. Calculus Notes
  2. Sets
  3. Combinatorics
  4. Conditional Probability
  5. Bayes鈥� Theorem
  6. Random Variables
  7. Conditional Probability for Random Variables
  8. Mean
  9. Variance and other Moments
  10. Percentiles
  11. Mode
  12. Joint Distributions
  13. Uniform Distribution
  14. Marginal Distribution
  15. Joint Moments
  16. Covariance
  17. Conditional Distribution
  18. Conditional Moments
  19. Double Expectation Formula
  20. Binomial Distribution
  21. Negative Binomial Distribution
  22. Poisson Distribution
  23. Exponential Distribution
  24. Normal Distribution
  25. Bivariate Normal Distribution
  26. Central Limit Theorem
  27. Order Statistics
  28. Moment Generating Functions
  29. Probability Generating Functions
  30. Transformations
  31. Transformations of Two or More Variables