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It builds foundational probability tools for quantitatively assessing risk, assuming calculus proficiency. The syllabus-driven coverage closely follows Ross’s A First Course in Probability (8th edition) and introduces set theory, counting and combinatorics, core probability definitions, conditional probability and independence, discrete and continuous random variables, joint distributions, expectation properties, limit theorems, and risk management. 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Finan Arkansas Tech University  \n􀀍cAll Rights Reserved November 2013 Syllabus Last updated  \nJuly 8, 2014  \nIn memory of my parents  \nAugust 1, 2008 January 7, 2009  \nPreface  \nThe present manuscript is designed mainly to help students prepare for the Probability Exam (Exam P/1), the 􀀌rst actuarial examination administered by the Society of Actuaries. This examination tests a student's knowledge of the fundamental probability tools for quantitatively assessing risk. A thorough command of calculus is assumed.  \nMore information about the exam can be found on the webpage of the Society [of Actuaries ](of Actuaries www.soa.org)[www.soa.org](of Actuaries www.soa.org).  \nProblems taken from previous exams provided by the Society of Actuaries will be indicated by the symbol z:  \nThe 􀀍ow of topics in the book follows very closely that of Ross's A First Course in Probability, 8th edition. Selected topics are chosen based on July 2013 exam syllabus as posted on the SOA website.  \nThis manuscript can be used for personal use or class use, but not for commercial purposes. If you 􀀌nd any errors, I would appreciate hearing from you: m􀀌nan@atu.edu  \nThis manuscript is also suitable for a one semester course in an undergraduate course in probability theory. Answer keys to text problems are found atthe end of the book.  \nMarcel B. Finan Russellville, AR August, 2013  \nii PREFACE  \nContents  \nPreface i  \nA Review of Set Theory 5  \n1 Basic De􀀌nitions ........................... 6  \n2 Set Operations ............................ 14  \nCounting and Combinatorics 27  \n3 The Fundamental Principle of Counting .............. 27  \n4 Permutations ............................. 33  \n5 Combinations ............................. 38  \nProbability: De􀀌nitions and Properties 45  \n6 Sample Space, Events, Probability Measure ............ 45  \n7 Probability of Intersection, Union, and Complementary Event .. 54  \n8 Probability and Counting Techniques ................ 63  \nConditional Probability and Independence 69  \n9 Conditional Probabilities ....................... 69  \n10 Posterior Probabilities: Bayes' Formula .............. 76  \n11 Independent Events ......................... 86  \n12 Odds and Conditional Probability ................. 95  \nDiscrete Random Variables 99  \n13 Random Variables .......................... 99  \n14 Probability Mass Function and Cumulative Distribution Function 106  \n15 Expected Value of a Discrete Random Variable .......... 114  \n16 Expected Value of a Function of a Discrete Random Variable .. 122  \n17 Variance and Standard Deviation ................. 129  \n2 CONTENTS  \nCommonly Used Discrete Random Variables 135  \n18 Bernoulli Trials and Binomial Distributions ............ 135  \n19 The Expected Value and Variance of the Binomial Distribution . 143  \n20 Poisson Random Variable ...................... 149  \n21 Poisson Approximation to the Binomial Distribution ....... 156  \n22 Geometric Random Variable .................... 161  \n23 Negative Binomial Random Variable ................ 168  \n24 Hypergeometric Random Variable ................. 175  \nCumulative and Survival Distribution Functions 181  \n25 The Cumulative Distribution Function .............. 181  \n26 The Survival Distribution Function ................ 194  \nCalculus Prerequisite 199  \n27 Graphing Systems of Linear Inequalities in Two Variables .... 199  \n28 Improper Integrals .......................... 203  \n29 Iterated Double Integrals ...................... 214  \nContinuous Random Variables 223  \n30 Distribution Functions ....................... 223  \n31 Expectation and Variance ...................... 234  \n32 Median, Mode, and Percentiles ................... 249  \n33 The Uniform Distribution Function ................ 256  \n34 Normal Random Variables ..................... 261  \n35 The Normal Approximation to the Binomial Distribution .... 270  \n36 Exponential Random Variables ................... 274","cbCaidIpBzKMjYWK","https://ap.wps.com/l/cbCaidIpBzKMjYWK","pdf",2836902,597,"English","# Preface\n# A Review of Set Theory\n## Contents\n## Counting and Combinatorics\n## Probability: Definitions and Properties\n## Conditional Probability and Independence\n## Discrete Random Variables\n## Commonly Used Discrete Random Variables\n## Cumulative and Survival Distribution Functions\n## Calculus Prerequisite\n## Continuous Random Variables\n## Joint Distributions\n## Properties of Expectation\n## Limit Theorems\n## Risk Management and Insurance\n# Sample Exam 1\n# Sample Exam 2\n# Sample Exam 3\n# Sample Exam 4\n# Answer Keys\n# Bibliography\n# Index","[{\"question\":\"What is this manuscript designed to prepare students for?\",\"answer\":\"It is designed to help students prepare for the Probability Exam (Exam P/1), the first actuarial examination administered by the Society of Actuaries.\"},{\"question\":\"What knowledge is assumed before studying the course?\",\"answer\":\"A thorough command of calculus is assumed, and the text begins with a review of set theory for foundational probability concepts.\"},{\"question\":\"How closely does the book’s topic order follow existing coursework?\",\"answer\":\"The flow of topics follows very closely that of Ross’s A First Course in Probability, 8th edition, with selected topics chosen based on the July 2013 exam syllabus.\"}]","A Probability Course for the Actuaries - A Preparation for Exam P/1 | PDF",1790493256,1504]