Fall 2005 - Exam P (Probability) Exam P Probability The examination for this material consists of 3 hours of multiple-choice questions and is identical to CAS Exam 1. Exam P will be offered as a computer-based test in September 2005. Details on this appear earlier in the catalog in the Exam P Computer-Based Testing Administration Details section. 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: 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 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 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