MTH3120: Elementary Probability (Spring 2023)

Instructor: Ivan Matic
Class website: imomath.com/bmath
email: Ivan.Matic@baruch.cuny.edu
Class time: MoWe 12:50PM - 2:05PM
Class location: online and B 10-130 (Zoom information)
Section code: DMWA
Office hours time: MoWe 11:40AM - 12:40PM
Office hours location: M: online; W: in person (Zoom information)
Grading formula
Quizzes: up to 25% *
Midterms: 50%
Final: 25% **
* If the scores from the proctored exams (midterms and final) are consistent with the scores from quizzes, then the quizzes will count 25% of the grade. If the scores from the proctored exams are significantly lower than the scores from the quizzes, then the scores from the quizzes will be replaced with the average score of the proctored exams.
** If a student receives a failing grade on the final exam, then the grading formula will not be used and the student will get F.

Announcement: Putnam Mathematical Competition at Baruch College

PDF with announcement

Content of the course

Prerequisite: MTH 2205, 2206, 2207, or 2610. Not open to students who have completed MTH 4120.
This course will introduce the student to the basic elements of discrete probability including: sample spaces, rules of probability, independence, conditional probability, Bayes' Theorem, discrete multivariate distribution, covariance, correlation and various special discrete distributions. It will also cover a small amount of integral calculus and introduce the student to the Normal distribution and the Central Limit Theorem. This course is not open to students who have completed MTH 3020 or MTH 3030 or MTH 4120.
Textbook: Warren B. Gordon: An Elementary Introduction to Probability, 4th Edition (2016), ISBN: 978-1535465144
Solutions to selected exercises: https://www.baruch.cuny.edu/math/probab4ed
Lecture notes and videos: https://imomath.com/bmath/index.cgi?page=m3120Notes

Learning goals

Upon completion of this course, students will be able to: describe the sample space of an experiment; enunciate Kolmogorov’s probability axioms, and use these axioms to prove basic probability theorems; state the law of total probability and Bayes’ Theorem, and use them to calculate conditional probabilities; explain and apply the concept of a random variable (discrete and continuous); use the distribution of a random variable to compute probabilities; construct discrete random variables and calculate the associated cumulative distribution function and probability mass function; recognize and apply common random variables (including binomial, geometric, negative binomial, Poisson, uniform, exponential, and normal random variables) to solve problems; define the probability moment generating functions, and use them to calculate probabilities and moments; apply properties of expectation and variance to solve problems; ascertain independence or dependence of a sequence of random variables and compute the covariance of a pair of random variables; determine the distribution of a function of a random variable; state Markov’s inequality, Chebyshev’s inequality, and the Central Limit Theorem and use these results to estimate tail probabilities..

Grading Policies

Quizzes

The quizzes contribute to \(25\%\) of the course grade. There will be 8 quizzes in total. The first quiz is "Academic Integrity Quiz" and is given during the first class. The due dates for the remaining assignments are maintained in the table on the course website. Some of the quizzes will be during in-person classes. Several of the quizzes will be administered through the course website.
The quizzes are shorter than the midterms and the final. However, they are treated as exams. The rules for the quizzes are the same as the rules for the exams. The problems must be done individually and without help from others. Students are not allowed to show the exam questions to others. It is illegal to post the questions on websites or public forums. Questions are confidential, copyrighted, and intellectual property of Baruch College. You do not have a permission to copy the questions and show them to anyone who is not an instructor at Baruch College.
With a well-documented reason, a student may miss two quiz during the semester. In that case the score for each of the missed quizzes will be replaced by the re-scaled score from the final exam.

Midterms

There are two written midterm exams (\(M_1\) and \(M_2\)). The score from each of the midterm exams contributes \(25\%\) to the grade. The midterms are scheduled for Wednesday, March 1, 2023 and Wednesday, April 19, 2023.

Grade and Curve

The course grade will be determined according to the formula \begin{eqnarray*}T &=& \frac14\mbox{min}\left\{H, 0.33\cdot M_1+0.33\cdot M_2+0.34\cdot F + 10\right\} \\ && + \frac14 M_1+\frac14 M_2+\frac14 F. \end{eqnarray*} In the end the curve will be used so that at least \(25\%\) of the class gets \(A\) and \(A-\), and at least \(50\%\) of the class gets the grade \(B-\) or higher.

Recording policies

Students who participate in this class with their camera on or use a profile image are agreeing to have their video or image recorded. If you are unwilling to consent to have your profile or video image recorded, be sure to keep your camera off and do not use a profile image. Likewise, students who un-mute during class and participate orally are agreeing to have their voices recorded. If you are not willing to consent to have your voice recorded during class, you will need to keep your mute button activated and communicate exclusively using the "chat" feature, which allows students to type questions and comments live.

Proctoring of exams

Students taking in-person or hybrid classes who fail to follow the vaccine mandate per CUNY policy will be subject to potential academic withdrawal that could also impact their financial aid and might not be eligible for refunds for the course.

The midterm exams, the final exam, and most of the quizzes are planned to be in person. Make sure that you plan accordingly and arrive on campus with sufficient time to comply with the requirements of the Campus Security. If the Campus Security does not grant you the access to the building because you failed to follow the rules and policies, you will receive 0 points for the missed exams.

Online exams

Some of the quizzes are planned to be during online classes. It is possible that due to an emergency some or all of the in-class exams are switched from in person to online mode. In those cases, the students will be required to have their cameras on during the exams. The students will not be allowed to access any online services or external websites with content that is in any way related to the course. In the case of online exams, the students will be allowed to access only these three web services: 1) the web page with exam questions; 2) the dropbox web interface to upload scanned work; and 3) the official college e-mail server in the case that student needs to contact the instructor.

Missed classes

If a student misses a class, it is his/her responsibility to find out the contents of the class, watch the video recording if it is made, and read the notes.

Course policies may be introduced, discussed, or clarified during the classes. A student cannot use a missed class as an excuse for not obeying the policies.

Missed exams

All students must take the written exams at the same time. This rule will be strictly enforced to ensure the fair grading.
In the case of a missed written in-class exam, the student will be required to submit a written appeal with a well-documented reason for missing the exam. If the appeal is approved, the re-scaled score on the final may be used as the score for the missed exam. Two missed midterms or three missed quizzes result in an automatic F.
The math department's policy states that any score on the final below 50% may result in an automatic failure in the course, regardless of scores received during the semester. Thus, students who miss the final will receive an F. In the case of an extraordinary circumstance resulting in the missed final, a student who had a term average of at least 55% may appeal to the Mathematics Department. If that appeal is accepted, the student may receive an INC grade. A student who misses the final and has term grade lower than 55% will receive F regardless.

Disability accommodations

To receive special accommodations for the lectures and exams, students with disabilities need to contact the Office of Services for Students with Disabilities at (646) 312‑4590. More information can be found at Student Disability Services Website.

Academic integrity

Any act of a student that provides an unfair advantage to themselves or an accomplice is dishonest. If during an exam a student has within reach an object that can be used to gain an unfair advantage, the student is violating academic honesty codes, regardless of whether the student is observed to use such object. For example, electronic devices (that include but are not limited to: phones, headphones, earbuds, smart watches, or smart glasses), even if turned off, cannot be on desks or on persons during exams.
Academic dishonesty will not be tolerated. Depending on the severity of the offense, cheating on an exam will result in a grade of 0 on that exam, or in a final course grade of D, or in a final course grade of F. Cheating on one of the quizzes will result in score 0 on all of the quizzes. All offenders will be reported to the Office of the Dean of Students who will assign an administrative punishment in addition to the academic punishment.