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Exam P Learning Outcomes: (Items to research in Wiki)

The purpose of this course of reading is to develop knowledge of the fundamental probability tools for quantitatively assessing risk. The application of these tools to problems encountered in actuarial science is emphasized. A thorough command of probability topics and the supporting calculus is assumed. Additionally, a very basic knowledge of insurance and risk management is assumed. A table of values for the normal distribution will be included with the examination.

LEARNING OUTCOMES Candidates 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 – Non Bayes Theorem • Bayes Theorem / Law of total probability

2. Univariate probability distributions (including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, chi-square, beta, Pareto, lognormal, gamma, Weibull, and normal).

• Probability functions and probability density functions • Cumulative distribution functions • Conditional probability • 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

Suggested Texts There is no single required text for this exam. The texts listed below may be considered as representative of the many texts available to cover material on which the candidate may be examined. Not all the topics may be covered adequately by just one text. You may wish to use more than one of the following or other texts of your choosing in your preparation. Earlier or later editions may also be adequate for review.

• A First Course in Probability (Seventh Edition), 2005, by Ross, S.M., Chapters 1–8. • Fundamentals of Probability (Third Edition), 2005, by Ghahramani, S., Chapters 1–11. • John E. Freund’s Mathematical Statistics with Applications (Seventh Edition), 2004, by Miller, I. Miller, M., Chapters 1-8. • Mathematical Statistics with Applications (Sixth Edition), 2002, by Wackerly, D., Mendenhall III, W. Scheaffer, R.,Chapters 1-7. • Probability for Risk Management, 1999, by Hassett, M. and Stewart, D., Chapters 1–11. • Probability: The Science of Uncertainty with Applications to Investments, Insurance and Engineering 2001, by Bean, M.A., Chapters 1–9.

Study Notes SNs for the Preliminary Education examinations are available on the SOA Web site under Exams and Jobs/Candidate and Exam Information/Fall Exam Session/Fall 2006 Basic Education Catalog – Study Notes Information. Hard copies may be purchased by using the Study Note and Published Reference order form in the back of the printed catalog or by downloading the form from the Fall Exam Session Web page. Code  Title P-11-06# P Introductory Study Note Tables for Exam P P-09-05   P Sample Exam Questions and Solutions P-21-05   Risk and Insurance