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
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 (Sixth Edition), 2001, 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.
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
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 (Sixth Edition), 2001, 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.