# MATH 4740 - Theory of Probability

Class information:

• The syllabus is here.

Study guides:

Test solutions:

Past lecture notes:

Homework:

 HW 1 Do these problems. Here are the solutions.(Save problems 9 and 10 until you have done HW 2) HW 2 Do these problems. Here are the solutions.   Also do problems 15, 18, 42 from here.   Also do these problems.   Here are the solutions. Test 1 covers HW 1 and HW 2 above HW 3 Do these problems. Here are the solutions. (Here's another way to do problem 9.)   Also do these problems.   Here are the solutions. HW 4 Do these problems. Here are the solutions.   Also do this problem.   Here is the solution. Test 2 covers HW 3 and HW 4 above HW 5 Do these problems. Here are the solutions. HW 6 Do these problems. Here are the solutions.Typo on problem 3(c): Should be E[X] = 50/16, E[X^2] = 170/16, Var(X) = 220/256 = 55/64, sigma = square root (55/64) ~ 0.927. 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.

Schedule and lecture notes:

 week Monday Wednesday 1 1/24- lecture notes 1/26 - lecture notes 2 1/31 - lecture notes 2/2 - lecture notes                  +        proof of theorem                    from class 3 2/7 - lecture notes                  +        proof of theorem            from class 2/9 - lecture notes                   +          birthday paradox                  table 4 2/14 - lecture notes                   +          proof of formula         for combinations            from class 2/16 - lecture notes 5 2/21 - lecture notes 2/23 - lecture notes 6 2/28 - lecture notes 3/2- lecture notes                +     proof of theorem           from class 7 3/7 - lecture notes 3/9 - TEST 1 8 3/14 - lecture notes                    +        proof of theorem            from class 3/16 - lecture notes 9 3/21 - lecture notes 3/23 - lecture notes                  +          pic from class Spring break 3/29 - HOLIDAY 3/31 - HOLIDAY 10 4/4- lecture notes 11 4/11 - lecture notes 4/13 - lecture notes 12 4/18 - lecture notes 4/20 - lecture notes 13 4/25 - TEST 2 4/27 - lecture notes 14 5/2 - lecture notes 5/4 - lecture notes 15 5/9 - lecture notes 5/11- lecture notes Finals week 5/16 - 5/18 - final2:30 - 4:30

Deck of cards:

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

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.

• 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.

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.

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.

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: