# Untitled
**Source**: https://teaching.scss.tcd.ie/wp-json/wp/v2/module/357
**Parent**: https://teaching.scss.tcd.ie/module/stu23501-probability-and-theoretical-statistics-i/
{"id":357,"date":"2021-08-12T11:10:26","date\_gmt":"2021-08-12T10:10:26","guid":{"rendered":"https:\/\/teaching.scss.tcd.ie\/?post\_type=module&p=357"},"modified":"2023-08-22T14:00:50","modified\_gmt":"2023-08-22T13:00:50","slug":"stu23501-probability-and-theoretical-statistics-i","status":"publish","type":"module","link":"https:\/\/teaching.scss.tcd.ie\/module\/stu23501-probability-and-theoretical-statistics-i\/","title":{"rendered":"STU23501 – Probability and Theoretical Statistics I"},"content":{"rendered":"\n
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| **Module Code<\/strong><\/td> STU23501<\/td><\/tr>| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **Module Name<\/strong> <\/td> Probability and Theoretical Statistics 1<\/a><\/td><\/tr>| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **ECTS Weighting<\/strong>**[**[1]<\/strong><\/a><\/strong><\/td> 5 ECTS <\/td><\/tr>| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **Semester taught<\/strong><\/td> Semester 1 <\/td><\/tr>| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **Module Coordinator\/s <\/strong><\/td> Professor Simon Wilson<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nModule Learning Outcomes <\/h2>\n\n\n\n On successful completion of this module, students will be able to: <\/p>\n\n\n\n LO1. Derive the probability space for simple experiments, and prove simple properties of probabilities from its definition; LO2. Identify when random variables are independent, and derive conditional distributions and expectations; LO3. Define the most common discrete and continuous random variables, and compute their moments and probabilities, moment and characteristic generating functions where appropriate; LO4. Define a multivariate distribution and calculate marginal and conditional distributions from it; LO5. State and prove the laws of averages and of central limit;<\/p>\n\n\n\nModule Content<\/h2>\n\n\n\n This is a rigorous development of probability theory from an axiomatic foundation, along with some more advanced topics. The topics covered are: \u2022 Events and probabilities \u2022 The laws of probability \u2022 Independence and conditional probability \u2022 Discrete random variables \u2022 Continuous random variables \u2022 Multivariate distributions & independence \u2022 Moment and characteristic generating functions \u2022 The law of averages and the central limit theorem \u2022 Examples and past exam questions<\/p>\n\n\n\n <\/p>\n\n\n\nTeaching and learning Methods <\/h2>\n\n\n\n Handouts and question sheets, as well as pre-recorded video lectures with accompanying lecture notes are available through Blackboard.\u00a0 <\/p>\n\n\n\nAssessment Details <\/h2>\n\n\n\n | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **Assessment Component<\/strong><\/td> **Brief Description<\/strong> <\/td> **Learning Outcomes Addressed<\/strong><\/td> **% of total<\/strong><\/td> **Week set<\/strong><\/td> Week Due<\/td><\/tr>| | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Examination <\/td> In person. To be completed in 2 hours<\/td> LO1, LO2, LO3, LO4, LO5<\/td> 100<\/td> n\/a<\/td> n\/a<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nReassessment Details<\/h2>\n\n\n\n In person examination (100%)<\/p>\n\n\n\nContact Hours and Indicative Student Workload<\/h2>\n\n\n\n | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | **Contact Hours (scheduled hours per student over full module), broken down by<\/strong>: <\/td> **33 hours<\/strong><\/td><\/tr>| | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Video lectures and reading notes<\/td> 33 hours<\/td><\/tr>| Laboratory<\/td> 0 hours<\/td><\/tr>| | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Tutorial or seminar<\/td> 24 hours<\/td><\/tr>| | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Other<\/td> 0 hours<\/td><\/tr>| | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | | **Independent study (outside scheduled contact hours), broken down by:<\/strong><\/td> **72 hours<\/strong><\/td><\/tr>| | | | | | | | --- | --- | --- | --- | --- | --- | | Preparation for classes and review of material (including preparation for examination, if applicable)<\/td> 41 hours<\/td><\/tr>| | | | | | --- | --- | --- | --- | | completion of assessments (including examination, if applicable)<\/td> 18 hours<\/td><\/tr>| | | | --- | --- | | **Total Hours<\/strong><\/td> **116 hours<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\nRecommended Reading List<\/h2>\n\n\n\n Probability: an Introduction by Grimmett and Welsh, published by Oxford University Press.<\/p>\n\n\n\n Introduction to Probability Models by Ross, published by Academic Press (10th edition or later).<\/p>\n\n\n\nModule Pre-requisites <\/h2>\n\n\n\n **Prerequisite modules:<\/strong> STU12501, STU12502<\/p>\n\n\n\n **Other\/alternative non-module prerequisites:<\/strong> e.g. programming languages, specified topics, etc.. This information will be particularly relevant for visiting students or students taking this module as an approved module (if applicable).<\/p>\n\n\n\n <\/p>\n\n\n\nModule Co-requisites <\/h2>\n\n\n\n None<\/p>\n\n\n\nModule Website<\/h2>\n\n\n\n [Blackboard<\/a><\/p>\n","protected":false},"excerpt":{"rendered":" (Semester 1, 5 ECTS) This is a rigorous development of probability theory from an axiomatic foundation, along with some more advanced topics.<\/p>\n","protected":false},"author":52,"menu\_order":0,"template":"","meta":[],"module\_category":[73,118,78],"class\_list":["post-357","module","type-module","status-publish","hentry","module\_category-s1","module\_category-stats-year-2","module\_category-visiting"],"\_links":{"self":[{"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/module\/357","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/module"}],"about":[{"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/types\/module"}],"author":[{"embeddable":true,"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/users\/52"}],"wp:attachment":[{"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/media?parent=357"}],"wp:term":[{"taxonomy":"module\_category","embeddable":true,"href":"https:\/\/teaching.scss.tcd.ie\/wp-json\/wp\/v2\/module\_category?post=357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](https://teaching.scss.tcd.ie/wp-json/wp/v2/module/\"https:\/\/tcd.blackboard.com\/webapps\/login\/\")****** |** | | | | |** |** | | | | | | | | |** |** | | | | | | | |** |** |** |** |** | |** | |** | |**](https://teaching.scss.tcd.ie/wp-json/wp/v2/module/\"#_ftn1\")**** | |** | |** |