First Actuarial Exam:
Probability

General information

This exam is jointly administered by the Society of Actuaries and the Casualty Actuarial Society. The Society of Actuaries calls this exam "Exam P, Probability". The Casualty Actuarial Society calls this exam "Exam 1, Probability".

This exam is a three-hour, multiple-choice examination. In May 2005, this exam will be offered in the traditional pencil-and-paper format. In September 2005, Exam 1 will be offered as a computer-based test. The purpose of this examination is to develop a knowledge of the fundamental probability tools for quantitatively assessing risk. The application of these tools to problems encountered in actuarial science is emphasized. Knowledge of calculus is assumed. A table of values for the normal distribution will be included with the examination booklet.

The material in this test comes from Math 447, Introduction to Probability and Statistics I. Registration information on the test and different rules, such as the use of calculators, can be found in the Basic Catalog of the actuarial societies.

As all the actuarial test, this is tough test. In order to prepare for this exam, you can take Math 449, Problem Solving in Actuarial Sciences, which is a course specially designed to prepare for this first actuarial exam. Math 447, Introduction to Probability and Statistics I, is required to take Math 449, Problem Solving in Actuarial Sciences. It is highly recommended that once you have passed Cal III, you take Math 447 during a Fall semester and then Math 449. in the Spring semester. You should be able to pass the first actuarial exam in May.

Learning Objectives

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
   • Law of total probability
   • Bayes' Theorem

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
   • 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

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Recommended study materials

• Arcones Manual for Exam P/Exam 1, by Miguel A. Arcones. Available at Actex Publications and The Actuarial Bookstore.

• Risk and Insurance.

• Web notes from CAS.

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Sample Questions

Here there are sample questions for the first actuarial exam: sample questions, solutions.

Here are the tables for the first actuarial exam: tables.

Here some old actuarial exams using the previous syllabus of the first actuarial exam (the current syllabus of the first actuarial exam does not cover Calculus):

sample test, May 2000, November 2000, May 2001, November 2001 and May 2003, (solutions).

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Party the Actuarial Association

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