MTH 452: Mathematical Statistics

Spring 2020, Updated 03/13/2020

University of Rhode Island, Department of Mathematics

INSTRUCTOR: Jonathan A. Chavez Casillas

E-MAIL: jchavezc@uri.edu

LECTURE TIMES: . None, Online Interaction

OFFICE HOURS: Via the Chat Rooms in Sakai (see below)

COURSE MATERIAL: Sakai

Brief Course Description: This is an introductory course in Mathematical Statistics. Theobjective is to know the fundamental tools of probability that are needed to understand statis-tics. Some topics that need to be mastered are Joint Distributions, Limit Theorems, Estima-tion, Confidence Intervals, Regression and Analysis of Variance. The course will possess mainlythree components:

• Review and Understanding of Probability: A brief review of the basic concepts inprobability and the introduction to new ones will be given. An important emphasis willbe put on conditional probability and independence as they are the foundation of modernprobability and statistics.

• Estimation, Testing and Confidence Regions: An exploration on the usage of prob-ability techniques used in statistics will be given. A critical idea will be to find parametersor regions for high probability, where successive repetition of the experiment will yield animportant estimate of where such parameter lies. This parameter can then be used toexplain a model from which the data comes from allowing us to then test hypotheses

• Learn the usage of R in Statistics: Basic techniques on how to explore, interpretand analyze data to perfrom statitic tests will be investigated. It will become critical tolearn how to use R as a tool to help in the visualization and understanding of the mostimportant concepts in mathematical Statistics.

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Required Textbook: “Probability and Mathematical Statistics: Theory, Applications, andPractice in R”. Mary C. Meyer. SIAM.

Grade Description: There will be two Midterms and a Cumulative Final Exam. All 3 examswill have 2 components: An in-class portion and a take-home portion. The grade will becomputed as follows:

Exam 1: 20% February 27thExam 2: 20% April 10th at 4pmHomework/Worksheet: 20% Once per week.Class Participation 10% See belowCumulative Final Exam: 30% May 5th at 11amPost-Reading worksheets Extra 15% See below

• Exams: Exam 1 will be a combination of an in-class portion and a take home portion.The in-class portion will feature a true/false section, a multiple choice section and openanswer questions. There is no partial credit for the true/false and multiple choice ques-tions; however, there will be partial credit in the open answer questions. If the studenthas a valid reason (as defined in the University Manual) a comparable examination priorto the missed exam will be administered. Also, see Make-up policy below.

Due to the suspension of face to face classes, Midterm 2 and, unless we return to face-to-face instruction, the Cumulative Final exam will be given as “take-home” exams. Thedue date for the Midterm 2 is Friday, April 10 at 4pm, while the Cumulative Final Examis due on Tuesday, May 5 at 11 am, respecting the final exam schedule at URI. Pleaseplan accordingly because between the delivery date of homework 7 and the Final examthere is a little over one week period.

Please print out midterm 2. Work the problems out in a separate piece of paper and whenready write cleanly the solutions on the printed exam.

Please upload 1 pdf to the Exam 2 / Final Exam Assignment in Sakai with the pagesin order, in the correct orientation and it should be clear and legible. I will not acceptother format than pdf, more than 1 file or a messy work. This exam is a reflection of yourwork, so please make sure you deliver a clean scanned single pdf in the correct order andorientation. Again, submission is in the “Assignments” tool/folder in sakai, which is

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the same one where you upload your homeworks and post-reading document.

The exam can be worked in pairs or individually. Please indicate who you are workingwith. If I find plagiarism and the other person is not listed as a teammate, both peoplewill receive a 0 automatically and a report to the Dean’s Office will be made.

• Grade distribution1:

92.00 - 100 A 68.00 - 70.99 C87.00 - 91.99 A- 64.00 - 67.99 C-82.00 - 86.99 B+ 60.00 - 63.99 D+78.00 - 81.99 B 55.00 - 59.99 D75.00 - 77.99 B- 0.0 - 54.99 F71.00 - 74.99 C+

• Homework: Homework (in the form of a worksheet) will be assigned at the end of eachweek. It is the student’s responsibility to complete all the assigned exercises and to go tooffice hours or ask in class if there are questions. Making the homework as consciously aspossible becomes of vital importance since the midterms and final’s exam content will beprimarily generated from the homework. The usual schedule and format for each work-sheet is as follows:

After a week of classes, a worksheet containing exercises related to that week’s materialwill be given. The worksheet will contain two type of exercises: practice and testingproblems. The practice problems will be problems whose solutions are on the backof the book (odd exercise numbers). The testing problems will be problems whosesolutions are not in the back of the book (even exercise numbers). Students will havea week to complete the worksheet and go to office hours and ask questions in class (if thequestion is too long or there are too many questions, students may be referred to officehours). The worksheet is due one week after it is provided. Finally, solutions to thetesting problems of the worksheets will be available on the course website (url can befound at the beginning of this document) after students submit their work.

The lowest grade will be dropped.

Please upload 1 pdf to the Corresponding Homework Assignment in Sakai withthe pages in order, in the correct orientation and it should be clear and legible. I will notaccept other format than pdf, more than 1 file or a messy work. The homework is a reflec-tion of your work, so please make sure you deliver a clean scanned single pdf in the correctorder and orientation. Again, submission is in the “Assignments” tool/folder in sakai.

• Class participation: Along the course, students will be asked to present some chaptersof the textbook and participate during other student’s presentation. A detailed account ofthe student participation will be recorded. Further, at the beginning of each class, some

1Different grades may be given for borderline cases, to the discretion of the instructor.

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questions will be asked by the instructor to verify whether students read the assignedmaterial before class. Your participation so far in the semester has been graded in Sakaiunder the item name in-class participation (I made personal notes on participationduring the semester to assign a grade, if you have questions about your grade, feel freeto e-mail me!). A new participation item called online participation will be added toSakai gradebook and it will reflect your participation via the Chat Rooms only! (seeChat Rooms below). Your 10% total participation will be taken as the maximum be-tween those two grades!

• Post-reading worksheets: As established in class before the spring break, I will providepre-reading worksheets WITHOUT SOULTIONS, SINCE THAT IS PART OFYOUR JOB, for the remaining of the month in March, but it is your job to complete(the now) post-reading worksheets/document on the month of April per our agreement (Ireinforce again that the idea is that you mimic my work and make it yours). In order toenforce the policy, I have added a 15% extra credit work to the grade (almost a midtermgrade!), but it is not free. The following rules will apply:

1. Each “class date” (as stated in the course calendar below), should have a post-readingdocument uploaded to the corresponding assignment folder in Sakai. I already haveset-up the folders. Please take a look under Assignments in sakai.

2. Your post-reading document should reflect work on the chapter. It should demonstratethat you read carefully and consciously the text and tried to extract the importantinformation provided in the chapter.

3. Each post-reading document will count up to 1.66% of the extra-credit grade (up toa maximum of 9) to make the 15% available.

4. If you just extract some parts of the textbook (specially verbatim text), omit criticalinformation (reflecting the fact that you performed a quick reading) or just “copy-paste text to “fulfill” the requirement, you will get flagged and that assignment willnot count towards your extra-credit. If you get flagged 3 times, you will LOSE ALLTHE 15% EXTRA-CREDIT. So, if you don’t have time to do a post-readingdocument or you don’t want to, please refrain from doing something “just for thesake of doing something”.

5. Each post-reading assignment should be uploaded as 1 pdf in with the pages in order,in the correct orientation and it should be clear and legible. I will not accept otherformat than pdf, more than 1 file or a messy work. This document is a reflection ofyour work and is not mandatory, so make sure you deliver a clean scanned single pdfin the correct order and orientation.

6. Post-reading documents are individual. If I notice plagiarism from someone else,you will immediately LOSE ALL THE 15% EXTRA-CREDIT.

• Chat Rooms: This is will be the main change in the course. Please go Sakaiand look on your tools the “Chat Room”. Click on it. Most likely you will besent to the General Questions Chat Room. In there, you will be able to postgeneral questions about the course, difficult issues not related to a particularchapter among any other general things. Please notice that in the upper left

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corner of the Chat Room. there is a tab/button that reads “Change Room”.Click on that and your will be displayed with a list of the Chat Rooms I havecreated. These Chat Rooms are divided by chapters. If you have any questionsregarding the material of a chapter, you NEED TO POST THE QUESTIONIN THAT CHAPTER’S CHAT ROOM. The way online participation will beconsidered is by posting questions and, more importantly, TO RESPOND TOOTHER STUDENT’S QUESTIONS. I will be moderating the discussion andI will check the Chat Room of that week’s chapters twice a day. Please do notemail me questions. Post them in the Chat Rooms.

Attendance and Course Expectations: The student is expected to attend all the lectureseven-though there is no official “roll call”. This is a very demanding course and it isexpected hard work from the students. Students are responsible for all missed work, regardlessof the reason for absence. It is also the student’s responsibility to get all missing notes andmaterial covered within that missed lecture. Moreover, the student is expected to:

• Clear Writing: All the student work presented to the instructor (quizzes, exams, home-work questions) should be legible and clean. No steps should be skipped when doing arational deduction.

• Homework: Do all the homework assigned even-though it is not graded. The fast paceof the class require that the student perform work out of class.

• Prepare for lecture: The student is expected to read the material of the class prior toattending. The different topics and fast pace require that the student reads the textbookbefore coming to class.

• Ask for questions: If the student does not understand some points of the lecture, thestudent is expected and encouraged to ask questions in lectures and attend office hours ifneeded.

• Standards of behavior: Students are responsible for being familiar with and adheringto the “Community Standards of Behavior: University Policies and Regulations” (found atweb.uri.edu/studentconduct/university-student-handbook). If the student arriveslate to class, he/she should not disrupt the class. All cell phones or any electronic devicesmust be turned off.

Make up policy: As mentioned above, there are no make-up exams or quizzes. However,students who plan to be absent from classes or examinations for religious holy days that tradi-tionally preclude secular activity (see 6.20.11 for how such information is made available) shalldiscuss this with the appropriate instructor in advance of the holy day. In these cases a com-parable alternative examination will be administered before the scheduled time.Also, students who expect to be absent from classes or examinations for University sanctionedevents shall discuss this with the instructor at least one week in advance of the sanctioned

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event. For these purposes University sanctioned events shall be those events approved for classexcuses by the Provost and Vice President for Academic Affairs, a Vice President, a Dean, orthe Director of Intercollegiate Athletics. No event shall be regarded as University sanctioneduntil the Provost and Vice President for Academic Affairs has been notified. Disagreementsover the validity of an event being categorized as University sanctioned shall be mediated by theProvost and Vice President for Academic Affairs. If agreement cannot be reached, the Provostand Vice President for Academic Affairs shall decide the matter and that decision shall be final.In these cases a comparable alternative examination will be administered beforethe scheduled time. Finally, when serious illness, accident, personal tragedy, or other seriousmatters prevent students from attending classes, taking examinations, or meeting deadlines,thextbfa comparable alternative examination will be administered before the scheduled time.Disagreements over the seriousness of an illness, accident, personal tragedy, or other seriousmatter may need to be mediated by the concerned instructor’s department chair, dean, or even-tually the Provost and Vice President for Academic Affairs. Either students or their instructorsmay seek such mediation. If an agreement cannot be reached, the Provost and Vice Presidentfor Academic Affairs shall decide the matter and his/her decision shall be final.

Electronic Devices and other policies: No electronic devices are allowed, except for note-taking devices (and being used for taking notes) and other particular electronic devices thatthe instructor allows.

Academic Honesty Policy: Cheating is defined in the University Manual section 8.27.10 asthe claiming of credit for work not done independently without giving credit for aid received,or any unauthorized communication during examinations. Students are expected to be honestin all academic work. Consequences for any charge of cheating or plagiarism will follow theguideline established in the University Manual 8.27.10-8.27.21, http://web.uri.edu/manual/chapter-8/chapter-8-2/.

Special Needs: Your access in this course is important. Please send me your Disability Ser-vices for Students (DSS) accommodation letter early in the semester so that we have adequatetime to discuss and arrange your approved academic accommodations. If you have not yet estab-lished services through DSS, please contact them to engage in a confidential conversation aboutthe process for requesting reasonable accommodations in the classroom. DSS in Kingston is lo-cated in room 302 of the Memorial Union, 401-874-2098, https://web.uri.edu/disability/,dss@etal.uri.edu.

Religious holidays: Students who plan to be absent from classes or examinations for religiousholy days that traditionally preclude secular activity (see 6.20.11 for how such information ismade available) shall discuss this with the appropriate instructor in advance of the holy day.In these cases a comparable alternative examination will be administered beforethe scheduled time.

Tentative Course Outline: The class schedule for the remainder of the semester is detailedas follows:

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Date Chapter Topic Pages Homework problems Announcements

03/24/20 35 – 37 Hypothesis Tests for Normal Populations 301 – 334

Hwk 4: 34.5, 34.10, 34.17, 34.18, 34.20, 35.1, 35.3, 35.4, 35.6, 35.9,

Homework 4 will have been sent before 03/19/20.

03/26/20 38 , 40 Hypothesis testing for 1) Paired-Sample Normal Dist. 2) Distribution-Free Samples

335 – 340 347 – 354

Hwk 5: 36.4, 36.7, 36.8, 37.3, 37.8, 37.14, 38.3, 38.6, 40.4, 40.7

Homework 4 is due on Friday 03/27/20 at 4 pm. Homework 5 is given to you between 03/27/20 - 03/28/20

03/31/20 41 – 42 CLT and Parameter Estimation 355 – 370

04/02/20 43 – 44 Maximum Likelihood Estimation (MLE) and Methods of Moments 371 – 386

Midterm 2:

Chapters 32, 34 – 44

Homework 5 is due on Friday 04/03/20 at 4pm. Midterm 2 is given to you between 04/02/20 – 04/03/20

04/07/20 45 – 46 Bayes Estimation and Consistency of Point Estimators 387 – 404

04/09/20 47 Modes of Convergence 405 – 415 and

Notes provided by me.

Hwk 6: 45.2, 45.4, 45.9, 46.2, 46.5, 46.8, 47.2, 47.3 47.11 and 1 problem supplied by me.

Midterm 2 is due on Friday 04/10/20 at 4pm. Homework 6 is given to you between 04/10/20 – 04/11/20

04/14/20 48 , 50 Quantifying uncertainty via Standard Error (SE) and Confidence Intervals (CI) and Evaluation of CI

417 – 428 435 – 440

04/16/20 51 – 52 Bootstrap CI and information using MLE 441 – 456

Hwk 7: 48.1, 48.6, 48.13, 48.16, 50.3, 50.8, 51.5, 51.6, 52.5, 52.6

Homework 6 is due on Friday 04/17/20 at 4pm. Homework 7 is given to you between 04/17/20 – 04/18/20

04/21/20 53 – 54 Sufficient Statistics and Uniformly Minimum Variance Unbiased Estimators (UMVUE)

457 – 474

04/23/20 56 – 57 Evaluating Hypothesis Testing and the Neyman-Pearson Lemma 481 – 494

Homework 7 is due on Friday 04/24/20 at 4pm. FINAL EXAM is given to you between 04/23/20 – 04/24/20

04/28/20 58 , 60 Likelihood Ratio Tests and Analysis of Variance (ANOVA)

495 – 504 515 – 524

FINAL DAY OF CLASSES. As you will see this material is ALSO included in the final exam. Don’t procrastinate on it.

05/05/20 FINAL EXAM IS DUE AT 11 AM. Check https://web.uri.edu/enrollment/final-exam-schedules/ for more information