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 necessary concepts for multiple integration or partial derivatives will be re-introduced in the course as needed.

Course Description: This course provides a calculus based introduction to probability (an emphasis on probabilistic concepts used in statistical modeling). Coverage includes basic axioms of probability, sample spaces, counting rules, conditional probability, independence, random variables (and various associated discrete and continuous distributions), expectation, variance, covariance and correlation, probability inequalities, the central limit theorem, the Poisson approximation and sampling distributions.

Learning Objectives: Develop a working knowledge of (a) the basic concepts in probability (mean, variance, covariance, conditional probability, independence, Bayes theorem, etc..) and (b) the basic probability models (the classical discrete and continuous random variables and their interpretation as modeling tools). Furthermore develop the understanding and the application of the limit theorems of probability: the law of large numbers, Poisson approximation, and the central limit theorem.

Grading scheme: Homework 40%, Exams 50% (5 exams at 10% each), Participation 10%

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.

Course requirements and expectations:

• The class is held synchronously on Zoom. Attendance is required. Please contact your instructor if you cannot attend the class synchronously.

• The classes home page are on Moodle: A one-stop-shop with all information about the course, links to online tools, deadlines, zoom class recordings for asynchronous viewing, class whiteboards, slides….

• The weekly homework will be done on Webassign which also contains an electronic copy of the textbook Mathematical Statistics with Applications, Authors: Wackerly, Mendenhall, Schaeffer (ISBN-13: 978-0495110811), Edition: 7th.

Two options to sign up for Webassign at

‣$78 for the class. A Keycode will be provided by your instructor to sign up.

‣If you have other classes which use Webassign or other Cengage products, you may consider purchasing Cengage Unlimited which give you access to several classes for a fixed price and also allow to borrow physical textbooks

Webassign STAT 515 signup is at http://www.cengagebrain.com/course/4843445

• There will be 5 short (evening) exams during the semester administered through Gradescope, essentially for each section of the book (the last, “final” exam covers the last two sections and will take place during the slot for the final exam. There will be a first mock exam to familiarize yourself with Gradescope.

Use you Umass email and Student ID to identify yourself on www.gradescope.com/

Your instructor will provide you with a Keycode to enroll in Gradescope

Weekly Calendar:

• Week 1: 2/1

‣ Topics: Syllabus, Sec. 2.1-2.5, Introduction, set theory, axioms of probability

• Week 2: 2/8 (Friday 2/12 is the last day to drop with no record)

‣Topics: Sec. 2.6-2.9, Probability and counting, laws of probability I

• Week 3: 2/15

‣Topics: Sect 2.10-2.12, 3.1, 3.2, laws of probability II, random variables

• Week 4: 2/22 (Wednesday 2/24 is a Wellbeing Wednesday)

‣Topics: Sec 3.3-3.5, 3.7, 3.8, discrete random variables I

‣EXAM #1 (section 2).

• Week 5: 3/1 (Monday 3/1 follows Wednesday schedule)

‣Topics: Sec 3.9, 3.11, discrete random variable II, moment generating function, Chebyshev’s inequality,

• Week 6: 3/8

‣Topics: Sec. 4.1, 4.2, 4.3 continuous random variables

• Week 7:3/15

‣Topics: Sec 4.4-4.7, continuous distributions

‣EXAM #2 (section 3).

• Week 8: 3/22

‣ Topics: 4.8-4.10, 5.1, 5.2, moment generating function and Chebyshev’s inequality for continuous random variables, multivariate random variables.

• Week 9: 3/29 (Monday March 29 is last day to drop with a “DR”

‣Topics: 5.3-5.6, marginal and conditional distribution, independence

• Week 10: 4/5

‣Topics: 5.7-5.9, 5.11, covariance, sum of random variables, conditional expectation

‣EXAM #3 (section 4)

• Week 11: 4/12 (Wednesday 4/14 is a Wellbeing Wednesday)

‣Topics: 6.1, 6.2, 6.3, functions of random variables I

• Week 12: 4/19 (Tuesday 4/20 follows Wednesday schedule)

‣Topics: 6.4-6.5, 7.1, functions of random variables II, sampling

‣EXAM #4 (section 5)

• Week 13: 4/26

‣ Topics: 7.2, 7.3, 7.5, central limit theorem and sampling

• Week 14: 5/3 (last day of class on Tuesday 5/4)

‣Topics: Review

‣ EXAM #5 (sections 6&7) during final exam time slot.

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. If a last-minute emergency occurs after the two-week deadline, contact me ASAP. 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.

Accommodation Statement: The University of Massachusetts Amherst is committed to providing an equal educational opportunity for all students. If you have a documented physical, psychological, or learning disability on file with Disability Services (DS), you may be eligible for reasonable academic accommodations to help you succeed in this course. If you have a documented disability that requires an accommodation, please notify me within the first two weeks of the semester so that we may make appropriate arrangements. Please visit https://www.umass.edu/disability/ for more information.

Academic Honesty Statement: Since the integrity of the academic enterprise of any institution of higher education requires honesty in scholarship and research, academic honesty is required of all students at the University of Massachusetts Amherst. Academic dishonesty is prohibited in all programs of the University. Academic dishonesty includes but is not limited to: cheating, fabrication, plagiarism, and facilitating dishonesty. Appropriate sanctions may be imposed on any student who has committed an act of academic dishonesty. Instructors should take reasonable steps to address academic misconduct. Any person who has reason to believe that a student has committed academic dishonesty should bring such information to the attention of the appropriate course instructor as soon as possible. Instances of academic dishonesty not related to a specific course should be brought to the attention of the appropriate department Head or Chair. Since students are expected to be familiar with this policy and the commonly accepted standards of academic integrity, ignorance of such standards is not normally sufficient evidence of lack of intent (http://www.umass.edu/dean_students/codeofconduct/acadhonesty/).

It is a violation of the University Code of Student Conduct to utilize a study site such as chegg.com or coursehero.com in order to upload, download or receive help on exams or assignments that do not permit consultation. Please note that the University of Massachusetts has resources that enable instructors to trace posts (both the original poster and those who read the posts) from study sites, and that in this course we maintain an ongoing review of such sites during all exams.