[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657333-105":59,"doc-detail-657333-en":130},{"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":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","lecture-2-probability-basics-and-random-variables","Lecture 2 - Probability Basics and Random Variables","","Econ 113 Lecture Module 2 introduces core probability concepts through structured examples and diagrams. It defines experiments, sample points, sample spaces, events, complements, and event spaces, then explains how to represent outcomes for coin-flip scenarios. The module covers probability as a 0-to-1 measure, methods for assigning probabilities, and notation for compound events using union (A ∪ B) and intersection (A ∩ B). It further introduces discrete and continuous random variables and key distributions.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/lecture-2-probability-basics-and-random-variables/657333/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/lecture-2-probability-basics-and-random-variables/657333.png","ImageObject",300,407,{"name":92,"@type":93},"Ivy","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is an experiment, a sample point, and a sample space in this lecture?","Question",{"text":112,"@type":113},"An experiment is any manipulation or observation of the world. A sample point is an outcome of the experiment, and the sample space is the collection of all possible outcomes.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are events and complements represented?",{"text":117,"@type":113},"An event is a collection of sample points, and it either happens or does not. The complement of event A, denoted AC, represents the outcomes where A does not occur.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you compute probabilities for compound events using union and intersection notation?",{"text":121,"@type":113},"The lecture uses Pr(A U B) to represent the probability that A or B (or both) occur. It uses Pr(A ∩ B) to represent the probability that both A and B occur.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657333,1793063975,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},549758252649,"https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819","Econ 113  \nLecture Module 2  \nContents  \n1. Experiments and definitions  \n2. Events and probabilities  \n3. Assigning probabilities  \n4. Probability of complements  \n5. Conditional probability  \n6. Statistical independence  \n7. Discrete random variables  \n8. Continuous random variables  \n9. Uniform Distribution  \n10. Normal Distribution  \nDefinitions  \nExperiment: Any manipulation of the world or observation of the world.  \n• Flipping a coin  \n• Randomized Drug trials  \nSample Point: An outcome of the experiment  \n• One sample point must occur  \n1. Heads or tails  \n2. Drug success or failure  \n• Sample points are mutually exclusive  \nSample space: Space of all possible outcomes  \nHow do we represent the sample space? Coin flip:  \n• S={H,T}  \n• Fair Coin  \nHow do we represent the sample space? Coin flip:  \n• S={H,T}  \n• Fair Coin  \nVenn diagram:  \n\n| H | T |\n| --- | --- |\n\n• The entire box is the space of all possible outcomes  \n• The space in “H” is the probability of H occurring.  \n• The space in “F” is the probability of F occurring.  \nTree diagram:  \n.5 .5  \nH T  \nEvent: A collection of sample points An event either happens or does not.  \n• One sample point is an event.  \n• A group of sample points is an event.  \n• The complement of an event is a way to represent the event not occurring.  \n• The complement of event A is denoted AC  \n• Suppose that event A is heads  \n– AC is tails.  \n• How do we represent the event space?  \n• New example: Flip a coin twice .  \n• Sample space?  \n• S={HH, HT,TH,TT}  \n• Suppose that event A is getting heads on exactly one of the two flips.  \n• Event space?  \nA={HT,TH}  \n• What is Ac?  \nAc ={HH,TT}  \nVenn Diagram  \n\n| HH | TH |\n| --- | --- |\n| HT | TT |\n\nTree diagram  \nH T  \nHH HT TH TT  \n• What is probability?  \nA numerical measure of how likely an event is to occur.  \n• What are the key properties of probability? Probabilities range from 0 to 1.  \n• How do we assign probabilities?  \n1. a priori classical method  \na priori is Latin for before  \n2. Empirical classical method  \n3. Subjective classical method  \nProbability of compound events  \n• Notation  \nPr(A or B)=Pr(A U B)  \nProbability that either A, B, or both A and B occur.  \n“Union” of A and B  \nPr(A and B)=Pr(A ∩ B)  \nProbability that both A and B occur.  \n“Intersection” of A and B  \nExample: Draw one care from a deck of cards  \nEvent A: Drawing a face card  \nEvent B: Drawing a spade  \nPr(A U B)=Pr(Draw either a face card or spade or both)  \nPr(A ∩ B)=Pr(Draw both a face card and a spade)  \n= Pr(Draw either a jack, queen, or king of spades)","cbCaiqCugzvozr2R","https://ap.wps.com/l/cbCaiqCugzvozr2R","pdf",380512,48,"English","# Experiments and definitions\n## Sample points, sample space, and events\n## Probability of compound events\n## Discrete and continuous random variables\n## Uniform distribution\n## Normal distribution","[{\"question\":\"What is an experiment, a sample point, and a sample space in this lecture?\",\"answer\":\"An experiment is any manipulation or observation of the world. A sample point is an outcome of the experiment, and the sample space is the collection of all possible outcomes.\"},{\"question\":\"How are events and complements represented?\",\"answer\":\"An event is a collection of sample points, and it either happens or does not. The complement of event A, denoted AC, represents the outcomes where A does not occur.\"},{\"question\":\"How do you compute probabilities for compound events using union and intersection notation?\",\"answer\":\"The lecture uses Pr(A U B) to represent the probability that A or B (or both) occur. It uses Pr(A ∩ B) to represent the probability that both A and B occur.\"}]","Lecture 2 - Probability Basics and Random Variables | PDF",1792977556,121]