MATH 4740 - Theory of Probability

Class information:

  • The syllabus is here.

Some old tests to get an idea of the testing style:

Homework: 

The highlighted parts are errors in the solutions.   Note that I mispelled "lose" throughout the solutions as "loose." 

  • HW 1: Problems and solutions.
  • HW 2: Problems and solutions.
  • HW 2: Do problems 15, 18, and 42 from here.
  • HW 2: Do problems 36 and 41 from "Chapter 2" from here.
  • HW 3: Problems and solutions.
    (Error in solutions: #8 should be 1/6 not 1/5)
  • HW 3: Here are some more problems and solutions.
  • HW 3: Do problem 11 from "Chapter 3" from here.  (Problem 11 starts on page 10.)
  • HW 4: Problems and solutions.
  • HW 4: Do problems 20 and 30 from here.  Do problem 79 from here.  Do problem 25 from here.
  • HW 5: Problems and solutions.
  • HW 6: Problems and solutions.
    (Error in solutions: 2(c) Var(X) = 2.5, sigma changes too)
  • HW 7: Problems and solutions.
    (Error in solutions: 1(b) This should be phi(-0.313) - phi(-0.581) = (1-phi(0.313))-(1-phi(0.581)) = phi(0.581)-phi(0.313) = 0.7190-0.6217=0.0973 )
  • HW 7: Do problem 23 from here.  Do problem 59 from here.  Do problem 4 from here.

Miscellaneous links:

Proofs:

  • A proof about constructing finite and countable probability spaces.

Deck of cards:

  • Here is what is in 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.

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 a video of the Monte Hall Problem appearing in the movie 21.

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 St. Petersberg paradox.
  • 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.

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.