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It assumes a thorough command of calculus and guides students through probability concepts, properties, and techniques. The study flow follows the topic order of Ross’s “A First Course in Probability,” covering sets, counting, conditional probability, random variables, distributions, joint behavior, expectation and variance properties, limit theorems, and relevant appendices. 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Finan Arkansas Tech University  \n􀀍cAll Rights Reserved Preliminary Draft Last updated  \nJanuary 26, 2011  \n2  \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 Actauries ](of Actauries www.soa.org)[www.soa.org](of Actauries www.soa.org).  \nProblems taken from samples of the Exam P/1 provided by the Casual 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 Probabiltiy.  \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.  \nThis project has been partially supported by a research grant from Arkansas Tech University.  \nMarcel B. Finan Russellville, AR May 2007  \n4 PREFACE  \nContents  \nPreface 3  \nBasic Operations on Sets 9  \n1 Basic De􀀌nitions ........................... 9  \n2 Set Operations ............................ 17  \nCounting and Combinatorics 31  \n3 The Fundamental Principle of Counting .............. 31  \n4 Permutations and Combinations ................... 37  \n5 Permutations and Combinations with Indistinguishable Objects . 47  \nProbability: De􀀌nitions and Properties 57  \n6 Basic De􀀌nitions and Axioms of Probability ............ 57  \n7 Properties of Probability ....................... 65  \n8 Probability and Counting Techniques ................ 74  \nConditional Probability and Independence 81  \n9 Conditional Probabilities ....................... 81  \n10 Posterior Probabilities: Bayes' Formula .............. 89  \n11 Independent Events ......................... 100  \n12 Odds and Conditional Probability ................. 109  \nDiscrete Random Variables 113  \n13 Random Variables .......................... 113  \n14 Probability Mass Function and Cumulative Distribution Function 119  \n15 Expected Value of a Discrete Random Variable .......... 127  \n16 Expected Value of a Function of a Discrete Random Variable .. 135  \n17 Variance and Standard Deviation ................. 142  \n6 CONTENTS  \n18 Binomial and Multinomial Random Variables ........... 148  \n19 Poisson Random Variable ...................... 162  \n20 Other Discrete Random Variables ................. 172  \n20.1 Geometric Random Variable ................ 172  \n20.2 Negative Binomial Random Variable ............ 179  \n20.3 Hypergeometric Random Variable ............. 187  \n21 Properties of the Cumulative Distribution Function ....... 193  \nContinuous Random Variables 207  \n22 Distribution Functions ....................... 207  \n23 Expectation, Variance and Standard Deviation .......... 220  \n24 The Uniform Distribution Function ................ 238  \n25 Normal Random Variables ..................... 243  \n26 Exponential Random Variables ................... 258  \n27 Gamma and Beta Distributions .................. 268  \n28 The Distribution of a Function of a Random Variable ...... 280  \nJoint Distributions 289  \n29 Jointly Distributed Random Variables ............... 289  \n30 Independent Random Variables .................. 303  \n31 Sum of Two Independent Random Variables ........... 314  \n31.1 Discrete Case ........................ 314  \n31.2 Continuous Case ....................... 319  \n32 Conditional Distributions: Discrete Case ............. 328  \n33 Conditional Distributions: Continuous Case ..","cbCaiehLhZNISfP7","https://ap.wps.com/l/cbCaiehLhZNISfP7","pdf",2399255,517,"English","# Preface\n# Basic Operations on Sets\n# Counting and Combinatorics\n# Probability: Definitions and Properties\n# Conditional Probability and Independence\n# Discrete Random Variables\n# Continuous Random Variables\n# Joint Distributions\n# Properties of Expectation\n# Limit Theorems\n# Appendix\n# Answer Keys\n# Bibliography","[{\"question\":\"What exam does this manuscript prepare for, and what does that exam test?\",\"answer\":\"It prepares for the Probability Exam (Exam P/1) by the Society of Actuaries. The exam tests knowledge of fundamental probability tools for quantitatively assessing risk.\"},{\"question\":\"What background is assumed before studying the material?\",\"answer\":\"The manuscript assumes a thorough command of calculus. It also suggests readiness with basic set notation, Venn diagrams, and operations such as unions, intersections, and complements.\"},{\"question\":\"How is the study content organized?\",\"answer\":\"The topic flow follows closely the order of Ross’s “A First Course in Probability.” The contents progress from sets and counting to probability definitions, conditional probability, random variables, joint distributions, expectation properties, and then limit theorems, followed by an appendix and answer keys.\"}]","A Probability Course for the Actuaries - A Preparation for Exam P/1 | PDF",1303]