Syllabus

Syllabus – Stat 315 online Summer2024 – download: https://umass-my.sharepoint.com/:b:/g/personal/jjeneral_umass_edu/EeNG0_A5Oa9JoN7WWYdtGJAB1OtgJqRgSA5byV-jR5So-Q?e=2Nit5D

        

Syllabus – Stat 315 (Stat 515 previously) online Summer 2024

Instructor: Joanna Jeneralczuk

Email: jjeneral@umass.edu

Office Hours: Online – Zoom (TBA)

Prerequisites Two semesters of single variable calculus (Math 131-132) or the equivalent. Math 233 is not required for this course, some necessary concepts for multiple integration or partial derivatives will be 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) and the beginning of statistical inference (continued in Stat516). 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, the central limit theorem, and sampling distributions. Introduction to basic concepts of estimation (bias, standard error, etc.) and confidence intervals.

Textbook

Mathematical Statistics with Applications 7th Edition Wackerly, Mendenhall, Schaeffer

ISBN-13: 978-0495110811

List of Topics Covered:

  1. Chapter 2: Probability 2.1-2.5 Introduction, set theory, axioms of probability

2.6-2.9, Probability and counting, laws of probability I, 2.10-2.12, laws of probability II, Conditional Probability and Independence, Law of total probability and Baye’s Rule, random sampling

  • Chapter 3: Discrete Random Variables and Their Probability Distributions: 3.1 – 3.9, 3.11 (Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson Probability Distributions, Moments and Moment Generating Functions, Tchebysheff’s Theorem.

3 Chapter 4: Continuous Variables and Their Probability Distributions: 4.1-4.10 Uniform, Normal, Gamma, Beta, Exponential, Chi-square Probability Distributions, Tchebysheff’s Theorem, Moments and Moment Generating Functions.

  • Chapter 5: Multivariate Probability Distributions: 5.1 – 5.8, 5.10 and 5.11 (Bivariate and Multivariate Probability Distributions, Marginal and Conditional Probability Distributions, Independent Random Variables, Expected Value of a Function of Random Variables, Covariance, Expected Value and Variance of Linear Functions , Bivariate Normal Distribution, Conditional Expectations)
  • Chapter 6: Functions of random Variables: 6.1-6.5 Method of Distributions of Function of Random Variables, Method of Transformation Functions, Method of Moment Generating Functions
  • Chapter 7: Sampling Distributions and the Central Limit Theorem: 7.1 – 7.3 Sampling distributions Related to the Normal Distribution, The Central Limit Theorem 7.4 (optional), 7.5 The Normal Approximation to the Binomial Distribution.

Calculator

I recommend purchasing a graphing calculator. A TI-83/84 or a TI-86 are recommended.

Homework

All homework will be done online using the homework platform WebAssign.

You do not need to purchase a hard copy of the textbook. WebAssign comes with a digital copy of the textbook. WebAssign access is the only requirement for the course

You will have free access to WebAssign for the first 6 days, but you eventually must purchase an access code. All your work under the free access will be saved and transferred to your permanent account. We recommend you do not purchase anything until you have read the full syllabus – which will be on the course Canvas page. UMass has negotiated a reduced price with the publisher and there are special instructions needed to get the reduced price on Canvas

You will need a class key to view and register for the homework, which you will find in the course’s Blackboard page, after you register for this class.

Quizzes, Midterm Exam and Final Exam

There will be 6 quizzes after each chapter that will be completed through your WebAssign account. Your lowest quiz score will be dropped.

The Mathematics and Statistics department, in accordance with the University of Massachusetts at Amherst, continues to promote the integrity and security of its courses. To further secure its courses, the department will require a proctored final exam in this course.

I will provide exam proctoring for this course. More details will be available on the course website when the time comes.

These exams will cover:

  • Midterm Exam: Quizzes after each chapter replace Midterm exam
  • Final Exam: Sections 5.1 – 5.6, 5.8 – 5.10, 5.11, 6.1 – 6.5, 7.1 – 7.3, 7.5. Students are expected to know the Moment Generating Functions material from Sections 3.9 and 4.9.

NOTE: Make-up exams will only be given in the case of family or medical emergency. Both situations will require official documentation

Grading

Your final grade will be determined using the following weights:

  • Final Exam 30%
  • Quizzes 35% (6 total, lowest 2 score dropped)
  • Homework 30%
  • Participation 5%

The following grading scale will be used for your final grade:

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

Participation

Class discussions are set up so that we do not all have to be on-line at the same time. We have scheduled office hours on Zoom and working problems sessions if you want to chat with your classmates or me. There are Discussions, where you can post any questions, even homework questions or help someone. You will want to come back to these discussions after the due dates to catch up on your classmate’s comments that were added after you added your own comments.

For full credit, you will need to add a “quality” contribution for each chapter — i.e. a response that expresses clear thinking, and that is relevant to the discussion, help someone, or participate in Zoom sessions.

Weekly Schedule

  • Week 1:
    • Review syllabus
    • Chapter 2: 2.1-2.12 Introduction, set theory, axioms of probability, counting rules, laws of probability I, laws of probability II
  • Week 2: Chapter 3: 3.1-3.5, 3.7-3.9, 3.11 discrete random variables I, discrete random variables II, moment generating function, Chebyshev’s inequality
  • Week 3:
    • Chapter 4: 4.1-4.10 continuous random variables, continuous distributions
    • Midterm Exam
  • Week 4: Chapter 5: 5.1-5.6 Moment generating function and Chebyshev’s inequality for continuous random variables, multivariate random variables, marginal and conditional distribution, independence
  • Week 5:
    • Chapter 5: 5.7-5.9, 5.11 Covariance, sum of random variables, conditional expectation
    • Chapter 6: 6.1-6.5 Functions of random variables
  • Week 6 + part of Week 7
    • Chapter 7: 7.1-7.3, 7.5 Sampling and Central Limit Theorem
    • Review
    • Final Exam

Exam Make-Up Policy

The following are examples of acceptable reasons for missing an exam:

  • Medical reasons: Absence from an exam due to medical reasons can be planned or unexpected. If planned, I will need to be notified in advance. If unexpected, you will need to contact me within a day of the missed exam. In either case, you will need to provide me with documentation. You need not disclose any details of the reason for a medical excuse, but there must be enough information to allow the absence to be excused.
  • Religious observances: State law and University regulations require that a student be excused from academic pursuits on days of religious observance. The regulations also require the student to notify the instructor, in writing in advance. The University provides a list of major observances here: http://www.umass.edu/umhome/events/religious.php

Drop, Withdrawal, and Incomplete

The last day to drop the course with no record is Tuesday, May 28 .The last day to withdraw from the course (only a “W” will appear on your transcript) is Friday, June 14 •Contact the Registrar’s Office for information regarding how to take the course using the Pass/Fail option. •A grade of “Incomplete” can be given only for a compelling reason (e.g. serious illness). To receive an incomplete, you must be passing the course.

Academic Honesty Policy 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. The procedures outlined below are intended to provide an efficient and orderly process by which action may be taken if it appears that academic dishonesty has occurred and by which students may appeal such actions.

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.

For more information about visit http://umass.edu/honesty

Disability Accommodation

The University of Massachusetts Amherst is committed to making reasonable, effective, and appropriate accommodations to meet the needs of students with disabilities and help create a barrier-free campus. If you have a disability and require accommodations, please register with Disability Services (161 Whitmore Administration building; phone 413-545-0892) to have an accommodation letter sent to your faculty. Information on services and materials for registering are also available on their website www.umass.edu/disability

Technical Support

If you need assistance with technical support to participate in this course, please review our Student Orientation & Resource Area or Contact 24/7 Support. You will have the option of email, live chat, or phone.