Pub Date : 2018-09-03DOI: 10.1201/9781315370576-10
M. Proschan, P. Shaw
{"title":"Conditional Probability and Expectation","authors":"M. Proschan, P. Shaw","doi":"10.1201/9781315370576-10","DOIUrl":"https://doi.org/10.1201/9781315370576-10","url":null,"abstract":"","PeriodicalId":424052,"journal":{"name":"Essentials of Probability Theory for Statisticians","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134083654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-03DOI: 10.1201/9781315370576-11
M. Proschan, P. Shaw
{"title":"Applications","authors":"M. Proschan, P. Shaw","doi":"10.1201/9781315370576-11","DOIUrl":"https://doi.org/10.1201/9781315370576-11","url":null,"abstract":"","PeriodicalId":424052,"journal":{"name":"Essentials of Probability Theory for Statisticians","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133154074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Laws of Large Numbers","authors":"M. Proschan, P. Shaw","doi":"10.1201/9781315370576-7","DOIUrl":"https://doi.org/10.1201/9781315370576-7","url":null,"abstract":"","PeriodicalId":424052,"journal":{"name":"Essentials of Probability Theory for Statisticians","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132616188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Size Matters","authors":"M. Proschan, P. Shaw","doi":"10.1201/9781315370576-2","DOIUrl":"https://doi.org/10.1201/9781315370576-2","url":null,"abstract":"","PeriodicalId":424052,"journal":{"name":"Essentials of Probability Theory for Statisticians","volume":"63 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123187381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Elements of Probability Theory","authors":"M. Proschan, P. Shaw","doi":"10.1201/9781315370576-3","DOIUrl":"https://doi.org/10.1201/9781315370576-3","url":null,"abstract":"","PeriodicalId":424052,"journal":{"name":"Essentials of Probability Theory for Statisticians","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125313083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"More on Convergence in Distribution","authors":"M. Proschan, P. Shaw","doi":"10.1201/9781315370576-9","DOIUrl":"https://doi.org/10.1201/9781315370576-9","url":null,"abstract":"","PeriodicalId":424052,"journal":{"name":"Essentials of Probability Theory for Statisticians","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133574224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Integration and Expectation","authors":"M. Proschan, P. Shaw","doi":"10.1201/9781315370576-5","DOIUrl":"https://doi.org/10.1201/9781315370576-5","url":null,"abstract":"","PeriodicalId":424052,"journal":{"name":"Essentials of Probability Theory for Statisticians","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131634384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Random Variables","authors":"M. Proschan, P. Shaw","doi":"10.1201/9781315370576-4","DOIUrl":"https://doi.org/10.1201/9781315370576-4","url":null,"abstract":"","PeriodicalId":424052,"journal":{"name":"Essentials of Probability Theory for Statisticians","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123224602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
the sequence after N is always within ε of the supposed limit a. In contrast, the notion of convergence becomes somewhat more subtle when discussing convergence of functions. In this note we briefly describe a few modes of convergence and explain their relationship. Since the subject quickly becomes very technical, we will state many of the fundamental results without proof. Throughout this discussion, fix a probability space Ω and a sequence of random variables (Xn)n∈N. Also, let X be another random variable.
{"title":"Modes of Convergence","authors":"M. Proschan, P. Shaw","doi":"10.1201/9781315370576-6","DOIUrl":"https://doi.org/10.1201/9781315370576-6","url":null,"abstract":"the sequence after N is always within ε of the supposed limit a. In contrast, the notion of convergence becomes somewhat more subtle when discussing convergence of functions. In this note we briefly describe a few modes of convergence and explain their relationship. Since the subject quickly becomes very technical, we will state many of the fundamental results without proof. Throughout this discussion, fix a probability space Ω and a sequence of random variables (Xn)n∈N. Also, let X be another random variable.","PeriodicalId":424052,"journal":{"name":"Essentials of Probability Theory for Statisticians","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133452025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Central Limit Theorems","authors":"M. Proschan, P. Shaw","doi":"10.1201/9781315370576-8","DOIUrl":"https://doi.org/10.1201/9781315370576-8","url":null,"abstract":"","PeriodicalId":424052,"journal":{"name":"Essentials of Probability Theory for Statisticians","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123851198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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