Syllabus Stat 519 Fall2020-1 PDF

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SYLLABUS FOR STAT 51900 CLASS NUMBER 23642 FALL 2020 INTRODUCTION TO PROBABILITY Instructor Dr Sean Peng Class time 3:00-4:15PM TR Office hour (virtual) 4:20-5:20PM TR (or by apt) Math Phone 317-274-6918 E-mail [email protected]

Department Math Sciences Class Room ICTC (IT) 077 Office LD 224 B Office phone 317-274-8070 URL www.math.iupui.edu/∼ hpeng

Course Format: • This section will be taught in a Hybrid class taught both on campus and online using Canvas (http://canvas.iu.edu). • This section is a 13-week course and will end by November 20, 2020. • This section will have in-person meetings on-campus. • This section will have a synchronous component, all students are expected to attend live Zoom lectures and participate during the lectures. • All students are expected to attend face-to-face or live zoom lectures and participate during the lectures. • This sections live zoom lectures will be recorded for later review. • The remaining lectures are pre-recorded and viewed asynchronously during the week. • 12 quizzes administered during the class times and un-proctored. • Three exams administered during the class times and un-proctored. • Face-to-face problem solving sessions by TA. • Virtual office hours. • Attendance randomly checked via chat on Zoom. Lectures At a face-to-face/live zoom lecture time (see pacing schedule at the end of syllabus for details), the live zoom lecture can be joined by clicking the “Live Zoom Lecture link in the left-hand navigation column of Canvas course site. All students in the classroom should wear face masks at all times. Students should also follow the seating chart to find their assigned seat number in the classroom, and should continue sitting in the same seat for the remainder of the semester. If a student wants to change seat then such information must be emailed to and approved by the instructor before the change happens, and the student should sit in the new seat for the remainder of the semester. Recorded lectures are in “Kaltura: Media Gallery” at the left-hand navigation column of Canvas course site. Prerequisite MATH 26100 (Multivariate Calculus) or equivalent. An optional problem solving session is on Fridays from ??:??-??:?? at ??. TA can reached at [email protected] if you have questions about problem solving (otherwise, talk to me). Course Description Students will learn the basic concepts of probability including random variables and their moments, common distributions, and limit laws. Very little knowledge of

statistics is required in the course. So it is suitable for students in mathematics, economics, business, etc. who do not wish to pursue a program in statistics. However, it is a required course for applied statistics masters and bio-stat PhD and math PhD with concentration in statistics, and so we will focus on concepts that are essential for statistical/bio-statistical applications. This course prepares you for STAT 52800 Mathematical Statistics, which uses the same textbook and is offered in the spring semester. Textbook R. V. Hogg, J. W. McKean and A. T. Craig (2005). Introduction to Mathematical Statistics, 8th ed. Upper Saddle River, NJ: Prentice Hall. ISBN 978-0-321-79543-4. Cell phones must not be used in class, quizzes and exams. Software S-Plus, SAS and R packages (available at www.R-project.org) Homework Daily homework is assigned in class. Homework will not be collected and graded. Completing all homework sets on time is absolutely essential in learning the material and getting ready for quizzes and exams. Quizzes Quizzes are given at the end of the quiz day for about 10 minutes (from 4:05-4:15PM) and are based on homework problems due that day. The quizzes will be closed book and closed notes. Each of the 10 quizzes is worth 20 points (4%). There will be absolutely no make-up quizzes. All quizzes together accounts for 200 points (40%). Exams There will be three closed-book exams (one sheet of formulas permitted) in this course based on materials covered up to the previous class day. Each exam is for 75 minutes and worth 100 points (20%). There will be no make-up exams. The third exam is the final exam. However, MS (Applied/Bio Statistics) and PhD (Biostatistics and Mathematics) students are required to take a closed-book comprehensive exam on materials of STAT 51900 and 52800. Grading The percentage point distribution will be as follows: Top ten of twelve Quizzes (200 points), Three Exams (300 points). There will NOT be any make-up. Your letter grade will be determined by referring your achieved percentage score to the following absolute scale: 90+ =A, 75+ =B, 60+ =C, 45+ =D, < 45 =F; with associated +’ or - at five point increments. Student Conduct Please refer to IUPUI Code of Student Rights, Responsibilities, and Conduct (http://studentcode.iu.edu/). Incompletes Grades of Incomplete will only be given in accordance with the university policy (http://www.registrar.iupui.edu/incomp.html). In particular, an incomplete cannot be given to a student who is not passing the course for whatever reason. No Class Attendance without Official Enrollment After the conclusion of the 100% refund period for the relevant term or session (http://www.bursar.iupui.edu/refunds.asp), all individuals attending classes on a regular basis MUST be officially enrolled in the class, attending the class based on formal arrangements to make up a prior grade of Incomplete, or enrolled as an auditor. One time visitors to classes may be allowed only on an exception basis with prior permission of the instructor. Withdrawals If you decide to withdraw from the course, be sure to process all paperwork by the appropriate deadlines outlined in the following table: Date First Week After First Week 1/2 mark of Semester 3/4 mark of Semester

Required Signature None Advisor Advisor and Instructor Associate Chair, LD 270

Official details can be found at the university web page. Important Dates (Full details can be found at the university web pages). Mon Aug. 24 Sun Nov. 22 Tue Dec. 22 Th Dec. 24

First day of classes Last day of classes Faculty deadline for submitting Fall 2020 grades Grades available in One.IU

Table 1: Tentative Schedule (The instructor reserves the right to make changes without notice) Date Aug. 25 Aug. 27 Sep. 01 Sep. 03 Sep. 08 Sep. 10 Sep. 15 Sep. 17 Sep. 22 Sep. 24 Sep. 29 Oct. 01 Oct. 06 Oct. 08 Oct. 13 Oct. 15 Oct. 20 Oct. 22 Oct. 27 Oct. 29 Nov. 03 Nov. 05 Nov. 10 Nov. 12 Nov. 17 Nov. 19

Day T R T R T R T R T R T R T R T R R T R T R T R T R T

Contents Introduction & Set Theory Set Theory & Probability Probability & Properties Conditional Probability & Independence Random Variables & Discrete RV Discrete RV & Transformations Transformation Continuous RV Expectation of Random Variables Important Inequalities Exam 1 Two Random Variables Bivariate Transformations Conditional Distributions & Expectations Independent Random Variables Transformations & Examples Extension to Several Random Variables Binomial, Poisson, Gamma, Beta Distributions Univariate & Multivariate Normal Central/noncentral t, χ2 & F distributions Exam 2 Distributions of Quadratic Forms Independence of Quadratic Forms Convergence in Probability & in Distribution Convergence in Distribution & Bounded in Probability Central Limit Theorems Exam 3

Readings Quiz 1.1 - 1.2 1.2 - 1.3 Quiz 1 1.3 1.4 Quiz 2 1.5-1.6 1.6 Quiz 3 1.7 Quiz 4 1.8-1.9 1.9-1.10 Quiz 5 2.1 2.2 2.3-2.4 2.5 2.6 2.6-2.7 3.1-3.3 3.4-3.5 3.6-3.7 9.8 9.9 5.1-5.2 5.2 5.3

Quiz 6 Quiz 7 Quiz 8 Quiz 9 Quiz 10

Quiz 11 Quiz 12...