# STAT 515: Statistics I

## Spring Semester 2019-20

Instructor: Professor Markos Katsoulakis, LGRT 1423G, E-mail: markos [at] math umass edu

Lectures: Tuesdays, Thursdays, 11:30AM - 12:45PM, online.

Office Hours: By appointment.

Discussion Sessions: On Piazza and by Zoom appointment with your Section's TA.

TA for Section 5: Yujian Wu

### Textbook

• Mathematical Statistics with Applications, Authors: Wackerly, Mendenhall, Schaeffer (ISBN-13: 978-0495110811), Edition: 7th. (this is NOT the international edition-if you are using the international edition, you need to always consult for your homework assignments with the library copies on reserve)

### Prerequisites

Two semesters of single variable calculus (Math 131-132) or the equivalent, with a grade of "C" or better in Math 132. Math 233 is recommended but not required for this course and any ecessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

### Homework

• There will be weekly homework. Discussion of homework and practice problems with fellow students is encouraged but you must submit your own work.

• The weekly homework will be typically of two types:

(a) online homework on Webwork (typically due every Wednesday or Friday evening - always check webwork for exact due dates/times), and

(b) Homework from the book (we use WebAssign after the course went online).

The two types of homework sets have equal weight in grading.

NOTE: I will not accept late homework. Two missed homework assignmentsa are allowed without penalty and accordingly the two lowest grades will be discarded in the evaluation of the final homework grade.

• ### Homework Assignments (from the book)

• Homework 1: Section 2.3 #2.3, 2.5, 2.7,2.8; Section 2.4 # 2.11, 2.12, 2.16, 2.19, 2.23; Section 2.5 # 2.30, 2.33. Due in class Jan. 30th.
• Homework 2: Section 2.6 # 2.43, 2.61; Section 2.7 #2.75, 2.77, 2.82; Section 2.8 #2.89, 2.93, 2.102; Due in class Feb. 6th.
• Homework 3: Section 2.9: #2.115, 2.120 Section 2.10 # 2.125, Section 3.1-3.2 # 3.6, Section 3.3 # 3.14, 3.15, 3.22. Due in class Feb. 13th.
• Homework 4: Section 3.4 # 3.38, 3.57, Section 3.5 # 3.66, 3.71, Section 3.7 #3.118, Section 3.8 # 3.125, 3.128, 3.138. Due Monday Feb 24, 12 noon (instructor's mailbox LGRT 16th floor).
• Homework 5: Section 3.9 # 3.145, 3.149, 3.151. Section 3.11 # 3.167, 3.175, 3.177. Due Friday Feb 28, 12 noon (instructor's mailbox LGRT 16th floor).
• Homework 6: Sections 4.1–4.3 #4.2, 4.16, 4.20 and 4.26, Due in class March 12th.
• Homework 7: Section 4.4: 4.51 Section 4.5: 4.69, 4.71, 4.73 Section 4.6: 4.91, 4.109 Section 4.7: 4.131 Due Monday, March 30th, WebAssign.
• Homework 8: Section 4.10: 4.147, 4.149, 4.151 Section 5.1-5.2: 5.7, 5.9, 5.11, 5.13, 5.15, 5.17 Due Friday, April 3rd, WebAssign.
• Homework 9: See Webassign Due 4/7/20, 11:59PM EST.
• Homework 10: See Webassign Due 4/9/20, 4PM EST.
• Homework 11-15:: see WebAssign Due: see WebAssign.
• To get full credit, make sure you justify all your answers, or refer to the appropriate Theorem

HOMEWORK SOLUTIONS: Solutions to (the previous week's) written homework assignements are discussed at the beginning of each discussion session.

### Grading (updated after the class went online)

• Final Exam 15%, Midterm 1 20%, Midterm 2 15%, Homework 50% (25% homework from book, 25% Webwork)
• The final exam will focus on topics covered after the Midterms.
• Grading scale: A 90-100, A- 87-90, B+ 83-87. B 79-83, B- 75-79, C+ 71-75, C 67-71, C- 63-67, D+ 59-63, D 55-59, F 0-55.

### Exams

• Midterm 1: Wednesday, March 4, Time & Rm: 7-9PM, GSMN0064 (Sections 5, 6, 7), ILCN151 (Sections 1, 2, 3, 4).
• Material for Midterm 1: Chapter 2 and Chapter 3, 3.1-3.8.
• Review for Midterm 1: During Help Sessions
• Midterm 2: Thursday, April 9, Time & Rm: 7-9PM, Webwork.
• Material for Midterm 2: Sections 3.9, 3.11, 4.1-4.10, 5.1 - 5.6. Note that moment generating functions section 4.9 is defered to the final.
• Review for Midterm 2: see available material on Moodle
• Final Exam: Tuesday, May 5, Webwork; Time: TBD
• Material for Final Exam : Sections 5.8-5.10, 5.11, 6.1-6.5, 7.1-7.3, 7.5, however students are expected to know the Moment Generating Functions material from Sections 3.9 and 4.9 (and all worked out examples therein).
• Review for Final: During Help Sessions
• NOTE: Make-up exams will only be given in the case of family or medical emergency. Both situations will require official documentation. No make-up exams will be given for any other reason.

### Course policies

If you have a University-approved conflict (see the link in this paragraph) with an exam, you must let your instructor know at least two weeks before the exam. A make-up exam might be scheduled to take place shortly after the regularly scheduled exam. If so, the make-up exam will be different than the original but cover the same material. You will need to fill out the following sheet signed by the Registrar's office, explaining to your instructor why you are entitled to a make-up. Make sure to not book any travel during exams, including the snow-make-up date for the final. Travel is not an excuse to miss the exam. If a last-minute emergency occurs after the two-week deadline, you will need to present to your instructor a note either from your medical provider for medical emergencies or from the Office of the Dean of Students for non-medical emergencies. If a last-minute emergency occurs after the two-week deadline, you will need to present to your instructor a note either from your medical provider for medical emergencies or from the Office of the Dean of Students for non-medical emergencies.

### Class Material by Section

• Chapter 2: All sections.
• Chapter 3: 3.1 - 3.9, 3.11+additional material on Probabilistic Inequalities(material provided)
• Chapter 4: 4.1-4 .10
• Chapter 5: 5.1 - 5.8, 5.10 and 5.11
• Chapter 6: 6.1, 6.2, 6.4+Example 6.5, 6.5
• Chapter 7: 7.1, 7.2 (only Theorems 7.1-2), 7.3, 7.4 (optional), 7.5

### Weekly Schedule

• Week 1: Review syllabus, 2.1-2.5 Introduction, set theory, axioms of probability
• Week 2: 2.6-2.9, Probability and counting, laws of probability I
• Week 3: 2.10-2.12, 3.1, 3.2, laws of probability II, random variables
• Week 4: 3.3-3.5, 3.7, 3.8, discrete random variables I
• Week 5: 3.9, 3.11, discrete random variable II, moment generating function, Chebyshev’s inequality, review for midterm I
• Week 6, Review, Midterm I on Wednesday, 4.1, 4.2, continuous random variables
• Week 7, 4.3-4.7, continuous distributions
• Week 8, 4.8-4.10, 5.1, 5.2, moment generating function and Chebyshev’s inequality for continuous random variables, multivariate random variables.
• Week 9, 5.3-5.6, marginal and conditional distribution, independence
• Week 10, 5.7-5.9, 5.11, covariance, sum of random variables, conditional expectation
• Week 11, Midterm II on Wednesday, Review for Midterm II, 6.1, 6.2, 6.3, functions of random variables I
• Week 12, 6.4-6.5, 7.1, functions of random variables II, sampling
• Week 13, 7.2, 7.3, 7.5, central limit theorem and sampling
• Week 14, Review for Final

### Old exams

Below are various exams, without solutions, from Stats 515 in previous semesters. Note that the format, such as number of problems, varies. This is because the course chair also varies. Moreover, the exams dates are not always at the same point in the semester. So for example, some material on midterm 1 from one class might appear on midterm 2 of another class.

• Here is a link to the Fall 2015 Midterm 1.
• Here is a link to the Spring 2016 Midterm 1.
• Here is a link to the Fall 2016 Midterm 1. (in draft form)
• Here is a link to the Spring 2017 Midterm 1.
• Here is a link to the Spring 2016 Midterm 2.
• Here is a link to the Fall 2016 Midterm 2.
• Here is a link to the Spring 2017 Midterm 2.
• Here is a link to the Fall 2015 Final.
• Here is a link to the Spring 2016 Final.
• Here is a link to the Fall 2016 Final.
• Here is a link to the Spring 2017 Final.
• Here are two quizzes from Fall 2015, which some students took instead of a Midterm 2 that semester. Quiz , Another Quiz .