Math 241

(Last updated Monday, May 24 at 3:40pm)

Meetings

The first class meeting will be on Monday, February 1 at 1:40pm.

After the first week of class, we will use Monday's class time as an office hour meeting 1:40–2:40pm and we will have a live class session on Wednesdays 1:40–2:40pm.

All meetings will occur on Zoom (Zoom Link).

Materials

Syllabus
Textbook: Grinstead, Charles M. and Snell, J. Laurie. Introduction to Probability.
Solutions to odd-numbered problems in the Grinstead–Snell book
Optional Textbook: Ross, Sheldon. A First Course in Probability.
Gradescope
Quiz Guide
Online calculators: WolframAlpha, Symbolab
Contact: You can always reach me via email at nicholas.vlamis@qc.cuny.edu. I will generally respond within 24 hours.
Math Tutoring Lab: there will be some tutoring available for 241 this semester (see below for details).

https://sites.google.com/a/qc.cuny.edu/qc-math-lab-online-tutoring/Please check that page frequently, as information there is subject to change at any time!In order to view that page, you MUST sign-in using your Queens College e-mail / CAMS account:On the first [Google sign-in] page, use your e-MAIL ADDRESS (including @qc.cuny.edu)On the second [Queens College log-in] page, give just your USER NAME (without @qc.cuny.edu), and your password.

Week 15 (5/17--5/21)

Reading: Section 8.2 page 316 and Section 9.3
Video 1 (Notes)

A short video discussing the Law of Large Numbers and the Central Limit Theorem in context of continuous random variables.

Course Evaluations

Please take a couple of minutes to submit an evaluation for the course.

Week 14 (5/10--5/14)

Reading: Section 5.2 pages 205-206 and 212-214, Section 6.3 pages 268-274
Video 1 (Notes) --- Watch by Wednesday, May 12

Go over standard important densities for continuous random variables: uniform, exponential, and normal.

Video 2 (Notes) --- Watch by Wednesday, May 12

Go over expected value and variance for continuous random variables.

Quiz 12 (Solutions)
Homework 13 --- Complete by Monday, May 17

This is the final homework assignment. The last quiz---based on this content---will be distributed on Monday, May 17

Please take a couple of minutes to submit an evaluation for the course.

Live Session Video (Notes)

Examples involving expected values of continuous random variables.

Week 13 (5/3--5/7)

Reading: Section 4.2 up to page 168
Video 1 (Notes) --- Watch by Wednesday, May 5

Introduction to the concept of conditional probability with continuous random variables and examples.

Video 2 (Notes) --- Watch by Wednesday, May 5

Introduction to independence in continuous random variables.

Quiz 11 (Solutions)

There was a significant typo on the first version of this quiz, so the deadline has been extended to compensate for my error.

Homework 12 --- Complete by Monday, May 10
Solutions to some of the problems from Homework 11
Live Session Video (Notes)

More examples of conditional probability with continuous random variables.

Week 12 (4/26--4/30)

Reading: Section 2.2 pages 55--68 (if interested, you can read Section 2.1 for more context).
Video 1 (Notes) --- Watch by Wednesday, April 28

Introduction to the concept of continuous random variables via examples.

Video 2 (Notes) --- Watch by Wednesday, April 28

A formal introduction to continuous random variables, including probability density functions and cumulative distribution functions.

Quiz 10 (Solutions)
Homework 11 --- Complete by Monday, May 3
Live Session Video (Notes)

Went over examples involving continuous random variable and defined the exponential distribution.

A quick video discussing graphing two-variable inequalities if you need a reminder.

Week 11 (4/19--4/23)

Reading: Pages 333-336
Video 1 (Notes) --- Watch by Wednesday, April 21

A detailed example on how the Central Limit Theorem is used in polling.

Video 2 --- Watch by Wednesday, April 21

A short discussion of how the Central Limit Theorem can used to price car insurance.

Quiz 9 (Solutions)
Homework 10 --- Complete by Monday, April 26
Live Session Video (Notes)

Discuss more examples using the Central Limit Theorem

Week 10 (4/12--4/16)

Reading: Section 9.2 (pages 343–344)
Video 1 (Notes) --- Watch by Wednesday, April 14

The central limit theorem.

Video 2 (Notes) --- Watch by Wednesday, April 14

Using the table in Appendix A.

Quiz 8 (Solutions)
Homework 9 --- Complete by Monday, April 19
Live Session Video (Notes)

Introduced continuity correction to CLT and discussed examples.

Week 9 (4/5--4/9)

Reading: Section 6.2 and Section 8.1
Video 1 (Notes) --- Watch by Wednesday, April 7 *Ignore the comment about the exam at the beginning of the video: this was recorded last semester.

Introduce and discuss properties of variance and standard deviation.

Video 2 (Notes) --- Watch by Wednesday, April 7

Chebyshev's inequality and the (weak) Law of Large Numbers.

Quiz 7 (Solutions)
Homework 8 --- Complete by Monday, April 12
Live Session Video (Notes)

Calculus review

Week 8 (3/15--3/19)

Reading: Section 6.1 pages 225–234
Video 1 (Notes) --- Watch by Wednesday, March 24

Introduce the definition of expected value, go over a few properties, and compute expected value for several standard distributions.

Video 2 (Notes) --- Watch by Wednesday, March 24

Continue with expectation.

Quiz 6 (Solutions)
Homework 7 --- Complete by Monday, April 5
Live Session Video (Notes)

Went over examples involving calculation expected values.

Week 7 (3/15--3/19)

Reading: pages 183–192 in Section 5.1
Video 1 (Notes) --- Watch by Wednesday, March 17

An overview and introduction to several important discrete probability distributions, including the uniform distribution, binomial distribution, geometric distribution, and negative binomial distribution.

Video 2 (Notes) --- Watch by Wednesday, March 17

Introduce the Poisson distribution.

Quiz 5 (Solutions)
Homework 6 --- Complete by Monday, March 22
Live Session Video (Notes)

Compared and contrasted the binomial and poisson distributions. Went over some examples of both.

Week 6 (3/8--3/12)

A lot of students have had/are having exams around this time, so I am only going to post one video to make sure everyone can keep/catch up.
Reading: the subsection Bayes' Formula in Section 4.1.
Video 1 (Notes) --- Watch by Wednesday, March 10

Introduce, derive, and go over examples of Bayes's Formula.

Quiz 4 (Solutions)
Homework 5 --- Complete by Monday, March 15
Live Session Video (Notes)

Went over examples of problems involving Bayes's formula, including the Monty Hall Problem.

Week 5 (3/1--3/5)

Reading: the Binomial Probabilities and Binomial Distribution subsections of Section 3.2.
Video 1 (Notes) --- Watch by Wednesday, March 3

Go over some conditional probability examples.

Video 2 (Notes) --- Watch by Wednesday, March 3

Introduce Bernoulii trials processes, prove a formula, and do an example.

Quiz 3 (Solutions)
Homework 4 --- Complete by Monday, March 8
Live Session Video (Notes)

Went over examples involving Bernoulli trials processes.

Week 4 (2/22--2/26)

Reading: Section 4.1 (Do not read the subsections dealing with Baye's probability and Baye's formula, those are for next week).
Video 1 (Notes)

Introduce conditional probability and independence.

Video 2 (Notes)

Introduce joint random variables, and use this to introduce the notion of an independent trials process.

Quiz 2 (Solutions)

Due to the irregular schedule last week, you have an extra day to complete this week's quiz, so that we can have our live session before its due date.

Homework 3 --- Complete by Monday, March 1.
Live Session Video (Notes)

Went over example problems involving permutations and combinations.

Week 3 (2/15--2/19)

Schedule Change Notice: The college is closed on Monday in observance of President's day. Office hours on Monday are cancelled, but Wednesday's class time will be treated as an office hour. Quiz 1 will be handed out on Wednesday at 3pm and will be due anytime on Friday. There is only one video for this week, since we would have lost a day during a regular in-person class.
Read the Poker Hands subsection of Section 3.2.
Video 1 (Notes) --- Watch by end of the week

Introduce the notion of combinations and derive basic formulae. Go over examples, including introducing poker hands.

Homework 2 --- Complete by Monday, February 22.
Quiz 1 (Solutions)

Make sure to read the Quiz Guide. Quiz 1 will covers the same material as Assignment 1.

Week 2 (2/8--2/12)

Read Section 1.2 pages 18--29. Makes sure to read the subsection labelled Odds. I won't go over this in class, but I expect you to know it.
Read Section 3.1 through subsection Permutations.
Many of the sections in the book end with a subsection entitled Historical Remarks. These subsections are never mandatory reading, but they are really interesting.
Video 1 (Notes) --- Watch by Wednesday, February 10

Continue discussion probability distribution functions. We give an example of an infinite discrete sample space with a probability distribution function. We end with discussing several properties of probability distribution functions.

Video 2 (Notes) --- Watch by Wednesday, February 10

We cover section 3.1 in the text. We discuss a basic counting technique and go over permutations.

Homework 1 --- Complete by Wednesday, February 17
Live Session Video (Notes)

Briefly introduced the notion of a random variable and then discussed counting and permutations. We went over the Birthday Problem (and found that two people had their birthday that day!).

In case you are interested, here is a link to the Birthday Problem Calculator I used in class. It may be helpful on future exercises.

Week 1 (2/1--2/5)

Quiz 0 — Due Friday, February 5
Random Walk Video (Not Required)

This PBS video does a nice job of explaining random walks, a cool phenomenon having many real-world applications; it is a nice foreshadowing of many of the topics that will appear in the class.

Video 1 (Notes) -- Watch by Wednesday, February 3

The video starts with a short discussion of the course and then goes over basic set theory definitions that will be used throughout the course.

Live Session Video (Notes)

We go over many of the basic definitions for discrete probability and discuss examples of probability distribution functions. Covers portions of Section 1.2 in the textbook.

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