MTH4120: Introduction to Probability
Instructor: Ivan Matic
Class time: MoWe 12:25PM - 2:05PM
Section code: JMWA
Office hours time: Monday 2:10PM - 4:10PM
Homeworks and quizzes: 25%
Content of the course
This course is an introduction to the theory of probability. Topics to be included are basic theorems of probability, permutations and combinations, binomial and multinomial theorems, random variables with densities, sequences of independent identically distributed random variables, method of moments, the moment-generating function, central limit theorem, and standard-type probability distributions. Not open to students who have completed MTH 3120.
Textbook: David F. Anderson, Timo Seppalainen, and Benedek Valko: Introduction to Probability, Cambridge University Press; 1 edition (November 2, 2017), 978-1108415859
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; examine and solve problems dealing with multivariate continuous probability distributions; recognize when a specific multivariate continuous probability distribution is applicable.
Homeworks and quizzes
The weekly homeworks and quizzes contribute to \(25\%\) of the course grade. Some of these assignments will be graded by students. \(80\%\) of the total homework grade will be based on correctness of the solutions that you submit for grading. The last \(20\%\) of the grade will be based on the quality of the grading and the feedback you provide to other students during your grading assignments.
There are 8 graded assignments that count as homeworks and quizzes. The first quiz is "Academic Integrity Quiz" and is given during the first class. The due dates for the remaining quizzes are maintained in the table on the website.
Homeworks are due 5 minutes before the class starts. In other words, at the time the class starts, students are already 5 minutes late to submit the homework and the submission will not be accepted. This rule will be strictly followed. The homework grade represents the ability of students to complete and submit the homeworks on time. The solutions will be posted shortly after the homework is collected, and late submissions would mean an unfair advantage to some of the students.
Once the homeworks are collected, they will be randomly electronically distributed to students for grading. You will have one week to finish grading the homework(s) that were assigned to you. For each of the problems you will give half the credit for completeness, if the student has attempted to solve the problem and has written some explanation. The other half of the credit is for correctness and exposition. After the grade is submitted, the computer will add up to 25 points to the grade (so that grade does not exceed 100).
At the end of the semester you will receive a grade for your grading. This will be a number from \(0\) to \(100\) and it will count as \(20\%\) of all homework scores. It will be written instead of the score for the homeworks 9 and 10. If you are a responsible grader you will receive \(100\) points on the homeworks 9 and 10. If you are late or miss your grading job, you will receive a lower score on the homeworks 9 and 10. In addition, if you were assigned to grade your own homework then you will also be punished by getting \(0\) points. This \(0\) is actually the grade that you have assigned to yourself by not grading your own homework.
With a well-documented reason, a student may miss one homework during the semester. In that case the score for the missed homework will be replaced by the re-scaled score from the final exam.
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 Monday, October 4, 2021 and Monday, November 8, 2021.
Grade and Curve
The course grade will be determined according to the formula
\[0.25\cdot H + 0.25 \cdot M_1+0.25\cdot M_2+ 0.25\cdot F.\]
In the end the curve will be used so that at least \(25\%\) of the class gets \(A\) and \(A-\), and at least \(30\%\) gets \(B+\), \(B\), and \(B-\).
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
Policy of the CUNY Chancellor: 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 and the final exam 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.
In the case that some or all of the in-class exams are switched from in person to online mode, 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. In the case of online exams, the students will be allowed to access only these three websites: 1) the website with exam questions; 2) the additional website to upload scanned work (such as dropbox); and 3) the official college e-mail server in the case that student needs to contact the instructor.
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 students cannot use a missed class as an excuse for not obeying the policies.
All students must take the written exams at the same time. This rule will be strictly enforced to ensure the fair grading.
Late homeworks will not be accepted. Homework is a grading instrument that needs to determine the ability of students to complete and submit the assignments correctly and on time.
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 exams or four missed quizzes (in the case there are 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.
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
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 or assignment will result in a grade of 0 on that exam or assignment, or in a final course grade of D, or in a final course grade of F. All offenders will be reported to the Office of the Dean of Students.