MATH 4740 - Theory of Probability

Syllabus:

syllabus

Study guides and practice tests:

Test 1 study guide and practice test from Fall 2023 and it's solutions.
Test 2 study guide and practice test from Fall 2023 and it's solutions.
<<Note that the practice test doesn't have topic 5 but it will be on your test.>>

Test solutions:

Test 1 and solutions

My notes:
These are the notes that I'm using to teach the class in case you want to look ahead.
The lecture notes for each day of class will be in the calendar below.

Topic 1 - Sets and Probability Spaces
Topic 2 - Counting
Topic 3 - Conditional Probability
Topic 4 - Random Variables
Topic 5 - Binomial Random Variables
Topic 6 - Variance
Topic 7 - Normal Approximation to Binomial Random Variables
Topic 8 - Continuous Random Variables

Homework:

HW 1	Do these problems. Here are the solutions.
HW 2	Do these problems. Here are the solutions.
HW 3	Do these problems. Here are the solutions. (Here's another way to do problem 12.)
HW 4	Do these problems. Here are the solutions.
HW 5	Do these problems. Here are the solutions.
HW 6	Do these problems. Here are the solutions. Note: The solutions above have a typo on problem 3(c). A corrected version is here.
HW 7	Do these problems. Here are the solutions. Do problem 23 from here. Do problem 4 from here (problems and solutions near the end of the pdf starting on page 15).
HW 8	Do these problems. Here are the solutions.

Fall 2024 - Calendar and Notes

Week	Monday	Wednesday
1		8/21 - lecture notes
2	8/26 - lecture notes	8/28 - lecture notes
3	9/2 - HOLIDAY	9/4 - lecture notes
4	9/9 - lecture notes	9/11 - lecture notes
5	9/16 - lecture notes	9/18 - lecture notes
6	9/23 - lecture notes	9/25 - lecture notes
7	9/30 - lecture notes	10/2 - lecture notes
8	10/7 - lecture notes	10/9 - TEST 1
9	10/14 - no notes	10/16 - lecture notes
10	10/21 - lecture notes	10/23 - lecture notes
11	10/28 - lecture notes	10/30 - lecture notes
12	11/4 - lecture notes	11/6 - lecture notes
13	11/11 - HOLIDAY	11/13 - TEST 2
14	11/18 - lecture notes	11/20 - lecture notes
	11/25 - HOLIDAY	11/27 - HOLIDAY
15	12/2 - lecture notes	12/4 - lecture notes
Finals week	12/9 - Final exam 2:30pm - 4:30pm	12/11

Miscellaneous links:

Standard Normal Distribution:

Here is a table of the values for the cumulative distribution function of the standard normal distribution. These will be used to approximated binomial random variables. Here is another table with both positive and negative values.

Deck of cards:

Here is what is in a standard deck of 52 cards.
My drawing of a standard deck of 52 cards.

Birthday Paradox:

Here is a handout that shows the birthday paradox calculations from class.

The Monte Hall Problem:

Here is the wiki page for the Monte Hall Problem.
Here is the Numberphile video on the Monte Hall problem.
Here is a video of the Monte Hall Problem appearing in the movie 21.

The St. Petersburg Paradox:

Here is the wiki page for the St. Petersburg paradox.
I wrote a program for this. Here is a pdf print out of it.

CA SuperLotto Plus:

Here is the main website for CA SuperLotto Plus.
Here are the past winning numbers.
Here is a video showing how the numbers are picked.

Roulette:

Here is the wiki page on Roulette.
Here is a picture of the American Roulette wheel and the European Roulette wheel.
This picture gives the different bets in American Roulette and the casino payouts.
Here is a video teaching you how to play Roulette (around 3:00 in he talks about the different bets one can make).

Craps:

Here is the wiki page for Craps.
Here is a video explaining how to play Craps.
Here is a handout of the craps table

Poker:

Here is the wiki page for Poker.
Here are the 5-card Poker hands.

Chuck-a-luck:

Here is the wiki page for Chuck-a-luck.
Here is a Vietnamese version of Chuck-a-luck.
Here is a British version of Chuck-a-luck.

Blackjack:

Here is the wiki page for Blackjack.
Here is a video of Austin Powers playing Blackjack.

Generating Random Numbers:

Numberphile episode 1 and episode 2
This guy made a muon-powered random number machine

Some theorems / problems / paradoxes / miscellaneous links:

Here is the wiki page on Probability Theory.
Here is the wiki page for the De Moivre-Laplace theorem.
Here is the wiki page for the Law of Large Numbers.
Here is the wiki page for the Central Limit Theorem.
Here is the wiki page for Random Walks.
Here is the wiki page for the Birthday problem.