[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-detail-399301-en":59,"doc-seo-399301-105":80},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":5,"data":60},{"doc_id":61,"user_id":62,"nickname":63,"user_avatar":64,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":66,"doc_content":67,"file_id":68,"file_url":69,"file_type":70,"file_size":71,"view_count":72,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":73,"language_code":74,"site_id":75,"html_lang":74,"table_of_contents":76,"faqs":77,"seo_title":78,"seo_description":66,"update_tm":79,"read_time":72,"preview_page_count":4},399301,687197207639,"Asher","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Exam1_Syllabus - Probability Exam Learning Objectives and Outcomes","Probability Exam learning objectives and outcomes for Exam 1 establish the required competencies for candidates in fundamental probability and risk assessment. The syllabus emphasizes quantitative tools, including core axioms, addition and multiplication rules, independence, mutual exclusivity, conditional probability, and Bayes theorem, supported by combinatorics. Coverage extends from univariate discrete and continuous random variables to multivariate discrete frameworks, including joint/marginal functions, moments, conditional distributions, order statistics, and applications such as linear combinations and the central limit theorem, plus examination credit waiver options.","The syllabus for this basic education requirement is defined in the form of learning objectives that set forth, usually in broad terms, what the candidate should be able to do in actual practice.  \nPlease check the “Syllabus Updates” section of the CAS Web Site for any changes to the Syllabus. The options for obtaining credit for this basic education requirement are listed below and in Examination Rules, C. Grades and Accreditation, Waivers of Examinations section of the Syllabus.  \nThe purpose of the syllabus 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 the supporting calculus is assumed. Additionally, a very basic knowledge of insurance and risk management is assumed.  \nThe Learning Objectives and Outcomes to follow have been sourced directly from the Syllabus: Probability Exam —September 2023, published by the Society of Actuaries.  \nLEARNING OUTCOMES  \n\n| 1. Topic: General Probability (23-30%) |\n| --- |\n| Learning Objectives |\n| The Candidate will understand basic probability concepts, combinatorics, and discrete mathematics. |\n| Learning Outcomes |\n| The Candidate will be able to:\u003Cbr>a) Define set functions, Venn diagrams, sample space, and events. Define probability as a set function on a collection of events and state the basic axioms of probability.\u003Cbr>b) Calculate probabilities using addition and multiplication rules.\u003Cbr>c) Define independence and calculate probabilities of independent events.\u003Cbr>d) Calculate probabilities of mutually exclusive events.\u003Cbr>e) Define and calculate conditional probabilities.\u003Cbr>f) Calculate probabilities using combinatorics, such as combinations and permutations.\u003Cbr>g) State Bayes Theorem and the law of total probability and use them to calculate conditional probabilities. |\n\n\n| 2. Topic: Univariate Random Variables (44-50%) |\n| --- |\n| Learning Objectives |\n| The Candidate will understand key concepts concerning discrete and continuous univariate random variables (including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, gamma, normal, lognormal, and beta) and their applications. |\n| Learning Outcomes |\n| The Candidate will be able to:\u003Cbr>a) Explain and apply the concepts of random variables, probability, probability density functions, and cumulative distribution functions.\u003Cbr>b) Calculate conditional probabilities.\u003Cbr>c) Explain and calculate expected value and higher moments, mode, median, and percentile.\u003Cbr>d) Explain and calculate variance, standard deviation, and coefficient of variation.\u003Cbr>e) Apply the concepts of deductibles, coinsurance, benefit limits, and inflation to convert a given loss amount from a policyholder into the corresponding payment amount for an insurance company.\u003Cbr>f) Calculate the expected value, variance, and standard deviation of both the loss random variable and the corresponding payment random variable upon the application of policy adjustments.\u003Cbr>g) Determine the sum of independent random variables (Poisson and normal) . |\n\n\n| 3. Topic: Multivariate Random Variables (23-30%) |\n| --- |\n| Learning Objectives |\n| The Candidate will understand key concepts concerning multivariate discrete random variables, the distribution of order statistics, and linear combinations of independent random variables, along with associated applications. |\n| Learning Outcomes |\n| The Candidate will be able to:\u003Cbr>a) Explain and perform calculations concerning joint probability functions and cumulative distribution functions for discrete random variables only.\u003Cbr>b) Determine conditional and marginal probability functions for discrete random variables only.\u003Cbr>c) Calculate moments for joint, conditional, and marginal discrete random variables.\u003Cbr>d) Calculate variance and standard deviation for conditional and marginal probability distributions for discrete random variables only","cbCaihFnLrLcKHJ1","https://ap.wps.com/l/cbCaihFnLrLcKHJ1","pdf",794204,13,"English","en",105,"# Learning Outcomes\n## 1. Topic: General Probability\n## 2. Topic: Univariate Random Variables\n## 3. Topic: Multivariate Random Variables\n# Options for Obtaining Exam 1 Credit","[{\"question\":\"What foundational probability topics are covered under General Probability?\",\"answer\":\"The syllabus covers basic probability concepts, combinatorics, discrete mathematics, set functions, Venn diagrams, sample spaces, events, probability axioms, and rules for addition and multiplication.\"},{\"question\":\"Which univariate random variable areas are included and what skills are expected?\",\"answer\":\"It includes key concepts for both discrete and continuous univariate random variables (e.g., binomial, Poisson, uniform, exponential, gamma, normal, lognormal, beta) and emphasizes computing distribution properties, moments, variance/standard deviation, and expected insurance and policy-adjusted payments.\"},{\"question\":\"How does the syllabus address multivariate random variables and probability calculations?\",\"answer\":\"It focuses on multivariate discrete random variables, joint and cumulative distribution functions, conditional and marginal functions, moments and covariance/correlation, order statistics, and probability/moments for linear combinations, including applications of the Central Limit Theorem.\"}]","Exam1_Syllabus - Probability Exam Learning Objectives and Outcomes | PDF",1790495949,{"code":4,"msg":81,"data":82},"ok",{"site_id":75,"language":74,"slug":83,"title":65,"keywords":84,"description":66,"schema_data":85,"social_meta":139,"head_meta":141,"extra_data":143,"updated_unix":144},"exam1_syllabus-probability-exam-learning-objectives-and-outcomes","",{"@graph":86,"@context":138},[87,101,121],{"@type":88,"itemListElement":89},"BreadcrumbList",[90,94,96,99],{"item":91,"name":92,"@type":93,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":95,"name":9,"@type":93,"position":14},"https://docshare.wps.com/document/",{"item":97,"name":20,"@type":93,"position":98},"https://docshare.wps.com/document/exam/",3,{"item":100,"name":65,"@type":93,"position":19},"https://docshare.wps.com/document/exam1_syllabus-probability-exam-learning-objectives-and-outcomes/399301/",{"url":100,"name":65,"@type":102,"image":103,"author":108,"headline":65,"publisher":110,"fileFormat":113,"inLanguage":74,"description":66,"dateModified":114,"datePublished":115,"encodingFormat":113,"isAccessibleForFree":116,"interactionStatistic":117},"DigitalDocument",{"url":104,"@type":105,"width":106,"height":107},"https://docshare.wps.com/thumbnails/exam1_syllabus-probability-exam-learning-objectives-and-outcomes/399301.png","ImageObject",300,407,{"name":63,"@type":109},"Person",{"url":91,"name":111,"@type":112},"DocShare","Organization","application/pdf","2026-11-08","2026-09-27",true,{"@type":118,"interactionType":119,"userInteractionCount":72},"InteractionCounter",{"@type":120},"ViewAction",{"@type":122,"mainEntity":123},"FAQPage",[124,130,134],{"name":125,"@type":126,"acceptedAnswer":127},"What foundational probability topics are covered under General Probability?","Question",{"text":128,"@type":129},"The syllabus covers basic probability concepts, combinatorics, discrete mathematics, set functions, Venn diagrams, sample spaces, events, probability axioms, and rules for addition and multiplication.","Answer",{"name":131,"@type":126,"acceptedAnswer":132},"Which univariate random variable areas are included and what skills are expected?",{"text":133,"@type":129},"It includes key concepts for both discrete and continuous univariate random variables (e.g., binomial, Poisson, uniform, exponential, gamma, normal, lognormal, beta) and emphasizes computing distribution properties, moments, variance/standard deviation, and expected insurance and policy-adjusted payments.",{"name":135,"@type":126,"acceptedAnswer":136},"How does the syllabus address multivariate random variables and probability calculations?",{"text":137,"@type":129},"It focuses on multivariate discrete random variables, joint and cumulative distribution functions, conditional and marginal functions, moments and covariance/correlation, order statistics, and probability/moments for linear combinations, including applications of the Central Limit Theorem.","https://schema.org",{"og:url":100,"og:type":140,"og:title":65,"og:site_name":111,"og:description":66},"article",{"robots":142,"canonical":100},"index,follow",{"doc_id":61,"site_id":75},1790721891]