[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-43255-en":3,"doc-seo-43255-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},43255,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",4,"Exam","Probability Through Problems","Probability Through Problems is an undergraduate problem book designed to accompany a course in probability while remaining suitable for independent study. It assumes basic algebra and calculus, plus elementary familiarity with set theory, sequences and series, one-variable functions, and derivatives. The book organizes each chapter into Problems, Hints, and Solutions, embedding definitions and key results within motivating exercises. It covers modeling random experiments, probability spaces, sigma fields, conditional probability and independence, random variables and distributions, expectation and variance, conditional expectation, characteristic functions, and applications of the law of large numbers and the central limit theorem.","Marek CapinskiTomasz Zastawniak  \n# Probability ThroughProblems\n\n·· ℃·  · :·  \n·门口门.·□  .门  。  \n·· ·.·  ·:  \n·   日.        :.:  :  :     ::  \nProblem Books in Mathematics  \nEdited by K.BencsáthP.R.Halmos  \nSpringer Science+Business Media,LLC  \nProblem Books in Mathematics              \nSeries Editors:K.A.Bencsáth and P.R.Halmos  \nPell's Equationby Edward J.Barbeau  \nPolynomialsby Edward J.Barbeau  \nProblems in Geometryby Marcel Berger,Pierre Pansu,Jean-Pic Berry,and Xavier Saint-Raymond  \nProblem Book for First Year Calculus  \nby George W.Bluman  \nExercises in Probabilityby T.Cacoullos  \nProbability Through Problems  \nby Marek Capinski and Tomasz Zastawniak  \nAn Introduction to Hilbert Space and Quantum Logic  \nby David W.Cohen  \nUnsolved Problems in Geometry  \nby Hallard T.Crof,Kenneth J.Falconer,and Richard K.Guy  \nBerkeley Problems in Mathematics(2nd ed.)  \nby Paulo Ney de Souza and Jorge-Nuno Silva  \nProblem-Solving Strategies  \nby Arthur Engel  \nProblems in Analysisby Bernard R.Gelbaum  \nProblems in Real and Complex Analysis  \nby Bernard R.Gelbaum  \nTheorems and Counterexamples in Mathematicsby Bernard R.Gelbaum and John M.H.Olmsted  \nExercises in Integration  \nby Claude George  \n(continued after index)  \n# Probability ThroughProblems\n\nWith 27 Figures  \nMarek CapińskiChair of Finance  \nNowy Sacz School of Business—NLUZielona 2733-300 Nowy SączPolandcapinski@wsb-nlu.edu.pl  \nSeries EditorsKatalin Bencásth  \nDepartment of MathematicsManhattan CollegeRiverdale,NY 10471USA  \nMathematics Subject Classification(2000):60-01,00A07  \nLibrary of Congress Cataloging-in-Publication Data  \nCapiński,Marek,1951-  \nProbability through problems/Marek Capiński,Tomasz Zastawniak  \np.cm.—(Problem books in mathematics)  \nIncludes bibliographic references and index.  \nISBN 978-1-4757-6291-4 ISBN 978-0-387-21659-1(eBook)DOI 10.1007/978-0-387-21659-1  \nIIL.Series.  \nISBN 978-1-4757-6291-4  \n◎2001 Springer Science+Business Media New YorkOriginally published by Springer-Verlag New York,Inc.in 2001Softcover reprint of the hardcover 1st edition 2001  \nTomasz ZastawniakDepartment of MathematicsUniversity of Hull  \nKingston upon HullHU67RXEnglandT.J.Zastawniak@hull.ac.uk  \nPaul R.Halmos  \nDepartment of MathematicsSanta Clara UniversitySanta Clara,CA 95053USA  \n1.Probability—Problems,exercises,etc.IZastawniak,Tomasz,1959 II.Title  \nQA273.25.C36  2000519.2'076—dc2100-056272  \nPrinted on acid-free paper.  \nAll rights reserved.This work may not be translated or copied in whole or in part without the writtenpermission of the publisher Springer Science+Business Media,LLC.  \nexcept for brief excerpts in connection with reviews or scholarly analysis.Use in  \nconnection with any form of information storage and retrieval,electronic adaptation,computersoftware,or by similar or dissimilar methodology now known or hereafter developed is forbidden.The use in this publication of trade names,trademarks,service marks,and similar terms,even if theyare not identified as such,is not to be taken as an expression of opinion as to whether or not they aresubject to proprietary rights.  \n## Preface\n\nThis book of problems has been designed to accompany an undergraduatecourse in probability.It will also be useful for students with interest inprobability who wish to study on their own.  \nThe only prerequisite is basic algebra and calculus.This includes someelementary experience in set theory,sequences and series,functions of onevariable,and their derivatives.Familiarity with integrals would be a bonus.A brief survey of terminology and notation in set theory and calculus isprovided.  \nEach chapter is divided into three parts:Problems,Hints,and Solutions.To make the book reasonably self-contained,all problem sections includeexpository material.Definitions and statements of important results areinterlaced with relevant problems.The latter have been selected to motivateabstract definitions by concrete examples and to lead in manageable stepstoward general results,as well as to provi","cbCaid4qCjcBSCLi","https://ap.wps.com/l/cbCaid4qCjcBSCLi","pdf",19555876,2,1,262,"English","en",105,"# Preface\n## Prerequisites and study approach\n## Chapter structure: Problems, Hints, Solutions\n## Overview of probability topics","[{\"question\":\"What prerequisites does the book require?\",\"answer\":\"The prerequisites are basic algebra and calculus, with elementary experience in set theory, sequences and series, one-variable functions, and derivatives. Familiarity with integrals is a bonus.\"},{\"question\":\"How is each chapter organized?\",\"answer\":\"Each chapter is divided into three parts: Problems, Hints, and Solutions. Problem sections include expository material with definitions and statements interlaced with relevant problems.\"},{\"question\":\"What does the book emphasize for self-study?\",\"answer\":\"Hints are designed to guide readers informally and help support self-study, with worked solutions intended for precision. Readers are advised to consult hints before solutions and to attempt solving problems independently first.\"}]",1783379270,660,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":28},"probability-through-problems","",{"@graph":36,"@context":84},[37,52,67],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/exam/",3,{"item":51,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/probability-through-problems/43255/",{"url":51,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":24,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":41,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-11","2026-07-06",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What prerequisites does the book require?","Question",{"text":74,"@type":75},"The prerequisites are basic algebra and calculus, with elementary experience in set theory, sequences and series, one-variable functions, and derivatives. Familiarity with integrals is a bonus.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How is each chapter organized?",{"text":79,"@type":75},"Each chapter is divided into three parts: Problems, Hints, and Solutions. Problem sections include expository material with definitions and statements interlaced with relevant problems.",{"name":81,"@type":72,"acceptedAnswer":82},"What does the book emphasize for self-study?",{"text":83,"@type":75},"Hints are designed to guide readers informally and help support self-study, with worked solutions intended for precision. Readers are advised to consult hints before solutions and to attempt solving problems independently first.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":91},[92,96,100,103,108,113,118,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":101,"slug":102},70,"exam",{"id":104,"doc_module":4,"doc_module_name":46,"category_name":105,"show_sort_weight":106,"slug":107},5,"Comic",60,"comic",{"id":109,"doc_module":4,"doc_module_name":46,"category_name":110,"show_sort_weight":111,"slug":112},6,"Technology",50,"technology",{"id":114,"doc_module":4,"doc_module_name":46,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":119,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":121,"slug":122},8,"Research & Report",30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":104,"slug":138},19,"General","general"]