Master Probability: Key Concepts for STAT 2400 Success
School
University of Manitoba**We aren't endorsed by this school
Course
STAT 2400
Subject
Statistics
Date
Dec 10, 2024
Pages
7
Uploaded by CountZebra4891
University of ManitobaDepartment of StatisticsSTAT 2400 – Introduction to Probability IWinter Term 2023Course DetailsCourse Number & Title:STAT 2400, Introduction to Probability ISection & CRN:Section A01, CRN: 11189Course Schedule:Monday/Wednesday/Friday, 9:30 to 10:30 a.m. (Slot 2),in room 201 Armes.Lab Schedule:Wednesday, 14:30 to 16:00, in room 201 Armes.Prerequisites:one of STAT 1150 (C) or STAT 2000 (B);one of MATH 1232 (C) or MATH 1700 (B).No special permissions are given with respect to prerequisites.Instructor Contact InformationInstructor:Alexandre LeblancOffice Location:367 Machray HallPhone:(204) 474-6273Email:Alex.Leblanc@umanitoba.caOffice Hours:Monday 13:30 - 15:00 and Thursday 9:30 - 11:00.I’m also generally available after class or by appointment.Changes/additions to be announced on UMLearn.Teaching Assistant (TA) Contact InformationTA:Tessa ReimerOffice Location:355 Machray HallEmail:reimer42@myumanitoba.caOffice Hours:Tuesday 11:30 - 12:30.Changes/additions to be announced on UMLearn.1
General Goals for this CourseThis course is meant to start your basic training in probability theory by providing a semi-formalintroduction to its most important basic concepts. As such, some goals for the course are to helpyou build and develop•a solid foundation in basic probability that you can rely on for your upper level courses inStatistics, Actuarial Mathematics and Data Science,•skills related to the understanding and writing of basic mathematical proofs,•analytical skills related to problem solving.In this course, you will have an opportunity to develop a solid intuition and understanding ofprobabilistic ideas, along with solid skills in calculus and applied mathematics. All these skills willbe essential to your success.The course is quite demanding and your success will depend heavily on your hard work and abilityto solve many practice problems yourself.For instance, getting the solutions from your friends(rather than doing the problems yourself), learning the course notes by heart and cramming forexams are typically not very successful strategies. Always remember that the work you do to getto a solution (including all the mistakes made along the way) is often more important than thesolution itself: you will learn more from the work and research you do to get to the answer thanfrom copying down a solution found online or in some textbook!Course DeliveryLecture Delivery:As we are transitioning back to in-person teaching, all the lectures andlabs for this course will be delivered synchronously, in a traditional class-room setting. Currently, there are no plans to have any remote lectures.COVID-19 Policy:Although that may change during the term, the current policy regardingCOVID-19 stipulates the following.•Proof of vaccination is no longer required to come to campus.•The existing masking mandate will continue: masks are requiredeverywhere on campus (except when outside).•There are two notable exceptions to the above rule:1. Instructors may choose to remove their mask when activelyteaching, provided a 2m distance can be maintained from stu-dents.2. Staff may remove their mask when seated at a cubicle-typeworkspace, provided there is a physical barrier to adjacentworkers (e.g., cubicle partition) or a minimum of 2m sepa-ration from others.Although KN95 masks are highly recommended, 3-ply medical masks arealso acceptable. In fact, masks are available for free to members of theUniversity community in many locations on campus.Please stay at home if you are feeling unwell. I will be posting scannednotes from class after each lecture in order to help students keep up withthe pace of the course even after missing a lecture.I’m happy to holdindividual meetings and office hours virtually via Zoom to accommodatestudents that are self-isolating.2
Textbook and Other MaterialsTextbook:The course will be based on•Weiss, N.A. (2006), A course in Probability, Pearson.Two copies of the textbook will be available on reserve at the ScienceLibrary. This being said, you should be able to get by without makinguse of the textbook if you carefully study the provided lecture materialsand occasionally read from the other references.Other references:The following are other useful references that will be available on reserveat the Science Library:•Ross, S.M. (2006), A First Course in Probability,•Ghahramani, S. (2005), Fundamentals of Probability with StochasticProcesses,•Roussas, G. (2007), Introduction to Probability.Other references that are downloadable in PDF through SpringerLinks andthe University of Manitoba Libraries are:•Pitman (1993),Probability,•Dekking, Kraaikamp, Lopuha¨a & Meester (2005),A Modern Intro-duction to Probability and Statistics,•Devore & Berk (2012),Modern Mathematical Statistics with Appli-cations.Other Materials:Lecture notes, practice problems, sample tests and exams, solutions, shortvideos and other materials will be added to the UM Learn portal regularly.Practice Problems:There are no assignments to be handed in for credit in this course, butopportunities to practice will be provided to you. First, a list of practiceproblems will be provided to you. You are free (and encouraged) to workin groups on the practice problems, but remember the work you do to getto a solution is more important than the solution itself:it is all aboutthe process needed to get to a solution, rather than the answer itself. So,getting the solutions from a classmate is not going to help you develop theskills you will be examined on.In order to help you find the motivation to work on your practice problems,each test/exam will ask for some small number of problems taken fromthose lists, in original or slightly modified form. In the pre-pandemic era,the number of problems taken from the lists was typically between two andfive on each test/exam, but usually closer to four.Practice Tests:You will also be provided with practice tests (with complete solutions). Itis expected that you use these practice tests as practice assessments: workon the questions like you would on a regular test, without looking at thesolutions. This will allow you to evaluate your level of readiness for writingyour test.3
Assessments and Grading SchemeFinal Mark:The final mark for the course will be obtained from the following rule.Tests (3)60%(best 30%, worst 10%, other 20%)Final Exam40%(covering all course content)The weights provided above will be adjusted for students that miss one or moretests. See below.Letter Grade:I normally use the following cutoffs when assigning letter grades:Letter GradeMark out of 100Letter GradeMark out of 100A+90-100C+65-70A80-90C60-65B+75-80D50-60B70-75Fbelow 50However, I might elect to use slightly lower thresholds for some letter grades ifI think they are more appropriate. I will not use higher thresholds.Caveat:To receive a passing grade in the course, you need to have completedand have received a passing grade on at least two of the four assessments.Tests and ExamTests:There will be three 75-minute tests, currently scheduled for February 8, March 15and April 5, all during the lab time slot between 14:30 and 16:00.Make-up tests will not be scheduled. In addition, if you miss a test, you will be as-signed a mark of zero unless you notify me by email within 48 hours of the scheduledtest.•If you miss one test, the final exam will count for 50% of your final mark forthe course, and the two other tests will be respectively worth 30 and 20% ofyour final mark.•If you miss two tests, the final exam will count for 70% of your final markfor the course, and the test you have written will be worth 30% of your finalmark.Do note the potential impact of the above caveat in these cases. For instance, youwill receive a grade of F if you miss all three tests. Also, you should drop the classif you are having significant health problems and, as a result, cannot keep up withthe course.Final Exam:The Final Exam will be scheduled by the Registrar’s office during theUniversity-wide examination period taking place on April 14-28, andshould normally be of a 3-hour duration.If you miss the final exam,you should contact a student advisor from your home Faculty within 48hours of the scheduled exam time.Grading timeline:Under normal circumstances, test results should be available within twoweeks of a test being written.4
Important DatesThe following dates are important as to how the course will progress throughout the term.DateInformationJan 9First classJan 11Lab is replaced by lectureJan 18First LabJan 20-23End of the registration revision periodFeb 8Test 1 (Modules 1 and 2)Feb 20-24Winter Term Break - no classes or labMar 15Test 2 (Modules 3 and 4)Mar 22Last day to VW the courseApr 5Test 3 (Module 5)Apr 7Good Friday - no classesApr 12Last lectureApr 14-28Final Examination PeriodThe dates and covered materials for the tests are tentative (and subject to change at my discretion).Changes are subject to Section 2.8 of the ROASS Procedure.Outline of Covered Topics and Approximate TimelineModule and TitleApprox. Duration (in weeks)1.Basic Concepts (Weiss, Chap. 1 and 2)2– Axioms of probability and basic probability rules2.Combinatorial Probability (Weiss, Chap. 3)1.5– Counting rules and probability calculations3.Conditional Probability and Independence (Weiss, Chap. 4)2– Conditional probability, Independence & the Bayes rule4.Discrete Random Variables (Weiss, Chap. 5)2.5– Discrete random variables and probability mass functions5.Continuous Random Variables (Weiss, Chap. 8)2.5– Continuous random variables, cdf, pdf6.Expected Values (Weiss, Chap. 7, 10, 11)2– Basic properties of expected values, mean and variance7.Additional Optional TopicsTime– Joint Distributions - many independent random variablespermitting– Central limit theorem5
Respectful Behaviour and Use of Technology in the ClassroomIt is expected that you conduct yourself professionally and do not distract your fellow students whilein the classroom. It is also a general University of Manitoba policy that all technology resourcesare to be used in a responsible, efficient, ethical and legal manner. Students should restrict theiruse of technology to those approved by the instructorfor educational purposes only.Electronicmessaging, email, social networking, gaming, etc. should be avoided during class time. Cell phonesshould be turned off. If a student is on call for emergencies, their cell phone should be in vibratemode and the student should leave the classroom before using it.Class CommunicationsThe University requires all students to activate an official U of M email account.You shouldbe using this for all communications between your and me (and, in fact anything related to theuniversity, including all your instructors). All these email communications should comply with theUniversity’s policy on electronic communication with students, which can be found atwww.umanitoba.ca/admin/governance/governing_documents/community/electronic_communication_with_students_policy.htmlWhen emailing me, please make sure to follow proper email etiquette: emails should start withan opening salutation, be written in complete English (or French) sentences and be signed withyour name and student number. I will generally reply to emails within 24 hours, depending on theurgency of the situation and my availability, except during weekends. Note that I will not divulgegrades over email.CopyrightsCopyrighted Materials:We will use copyrighted content in this course. I have ensured thatthe content I use is appropriately acknowledged and is copied in ac-cordance with copyright laws and University guidelines. Copyrightedworks, including those created by me, are made available for privatestudy and research and must not be distributed in any format with-out permission.In particular, note that you do not have permission to upload anycourse notes, tests, practice problems and tests, or any other handoutI will use for this course to any note sharing websites. Videos andother recordings available to you through UMLearn are meant foryour own personal use only.Lectures:No audio or video recording of lectures or presentations is allowedin any format, openly or surreptitiously, in whole or in part withoutmy permission.More details are available online atwww.umanitoba.ca/copyright/.6
Academic IntegrityThe value of a degree from the University of Manitoba is dependent on students and faculty strictlyupholding values of honesty and academic integrity in all their work. Academic dishonesty devaluesthe hard work and effort of students who are working honestly to achieve their degrees. For thesereasons, it is important that you understand the basics of academic integrity, what constitutesacademic dishonesty and what are its very serious consequences. Useful resources can be found atwww.umanitoba.ca/student/resource/student_advocacy/academicintegrity/students/a-to-i-what-is-academic-integrityandsci.umanitoba.ca/statement-on-academic-dishonesty/I generally expect students to hold themselves to the highest standards of academic integrity.Impersonation, plagiarism, and using unauthorized materials are all very serious offences. Whenin doubt, it is generally a good idea to contact your instructor to discuss what is and what isnot allowed. Asking is a sign of integrity, not a signal that you are planning to cheat. All yourinstructors expect you to follow the rules:ignorance is not an acceptable excuse for academicmisconduct.ROASS Schedule ASchedule “A” of theResponsibilities of Academic Staff with regards to Students(ROASS) policies ofthe University of Manitoba lists resources and policies for students. It is important that you famil-iarize yourself with these resources and policies. This document is available from the Department ofStatistics web page at:www.sci.umanitoba.ca/statistics/courses-and-programs/outlines.c Alexandre Leblanc, Department of Statistics, University of Manitoba.This document is dated January 4, 2023.7