sample-p - EXCERPTS FROM ACTEX STUDY MANUAL FOR SOA EXAM...

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© ACTEX 2006 SOA Exam P/CAS Exam 1 - Probability EXCERPTS FROM ACTEX STUDY MANUAL FOR SOA EXAM P/CAS EXAM 1 Table of Contents Introductory Comments Section 2 - Conditional Probability and Independence
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© ACTEX 2006 SOA Exam P/CAS Exam 1 - Probability TABLE OF CONTENTS INTRODUCTORY COMMENTS SECTION 0 - REVIEW OF ALGEBRA AND CALCULUS Set Theory 1 Graphing an Inequality in Two Dimensions 9 Properties of Functions 10 Differentiation 12 Integration 14 Geometric and Arithmetic Progressions 17 and Solutions 19 Problem Set 0 SECTION 1 - BASIC PROBABILITY CONCEPTS Probability Spaces and Events 29 Probability 33 and Solutions Problem Set 1 43 SECTION 2 - CONDITIONAL PROBABILITY AND INDEPENDENCE Definition of Conditional Probability 49 Bayes' Rule, Bayes' Theorem and the Law of Total Probability 51 Independent Events 55 and Solutions Problem Set 2 59 SECTION 3 - COMBINATORIAL PRINCIPLES Permutations and Combinations 73 and Solutions Problem Set 3 79 SECTION 4 - RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS Discrete Random Variable 83 Continuous Random Variable 84 Mixed Distribution 85 Cumulative Distribution Function 85 Independent Random Variables 90 and Solutions Problem Set 4 95 SECTION 5 - EXPECTATION AND OTHER DISTRIBUTION PARAMETERS Expected Value 101 Moments, Variance and Standard Deviation 103 Moment Generating Function 103 Percentiles, Median and Mode 105 and Solutions Problem Set 5 111
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© ACTEX 2006 SOA Exam P/CAS Exam 1 - Probability SECTION 6 - FREQUENTLY USED DISCRETE DISTRIBUTIONS Discrete Uniform Distribution 123 Binomial Distribution 123 Poisson Distribution 125 Geometric Distribution 128 Negative Binomial Distribution 129 Hypergeometric Distribution 130 Multinomial Distribution 131 Summary of Discrete Distributions 132 and Solutions Problem Set 6 133 SECTION 7 - FREQUENTLY USED CONTINUOUS DISTRIBUTIONS Continuous Uniform Distribution 145 Normal Distribution 145 Exponential Distribution 148 Gamma Distribution and Pareto Distribution 151 Lognormal, Beta, Weibull, and Chi-Square Distributions 152 Summary of Continuous Distributions 153 and Solutions Problem Set 7 155 SECTION 8 - JOINT, MARGINAL, AND CONDITIONAL DISTRIBUTIONS Definition of Joint Distribution 165 Marginal Distributions 168 Independence of Random Variables 1 1 ( Conditional Distributions 172 Covariance Between Random Variables 176 Moment Generating Function for a Joint Distribution 177 and Solutions Problem Set 8 183 SECTION 9 - TRANSFORMATIONS OF RANDOM VARIABLES Distribution of a Transformation of 205 \ Distribution of a Transformation of Joint Distribution of and 206 \] Distribution of a Sum of Random Variables 207 Distribution of the Maximum of Minimum of Independent 211 Ö\ ß \ ß ÞÞÞß \ × "# 8 Order Statistics 212 Mixtures of Distributions 214 and Solutions Problem Set 9 217 SECTION 10 - RISK MANAGEMENT CONCEPTS Loss Distributions and Insurance 235 The Normal Approximation to Aggregate Claims 240 Insurance Policy Deductible 243 Insurance Policy Limit 245 Proportional Insurance 246 and Solutions Problem Set 10 249 PRACTICE EXAM 1 271
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© ACTEX 2006 SOA Exam P/CAS Exam 1 - Probability PRACTICE EXAM 2 291 PRACTICE EXAM 3 313 PRACTICE EXAM 4 339 PRACTICE EXAM 5 359
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This note was uploaded on 03/29/2010 for the course STATISTICS 50 taught by Professor Diaz during the Spring '10 term at California State University , Monterey Bay.

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sample-p - EXCERPTS FROM ACTEX STUDY MANUAL FOR SOA EXAM...

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