Syllabus. Statistics 35b: Introduction to Probability with Applications to Poker.
Prof. Rick Paik Schoenberg.
FALL 2009.

Lectures: Tuesdays and Thursdays, 11am - 12:20pm, Geology 3656.

Office Hours: Mondays, noon to 12:50 pm, Math-Science 8965.

Email: frederic@stat.ucla.edu

Course webpage: http://www.stat.ucla.edu/~frederic/35b/F09

Description: Exploration of some main topics in introductory probability theory, especially discrete probability problems, that are useful in wide variety of scientific applications. Topics include conditional probability and conditional expectation, combinatorics, laws of large numbers, central limit theorem, Bayes theorem, univariate distributions, Markov processes, and Brownian motion. Examination of computer simulation in depth and discussion of computational approximations of solutions to complex problems using R, with examples of situations and concepts that arise naturally when playing Texas Hold'em and other games.

Grading:
Class participation (5%).
Homework (25%).
Computer project A (5%).
Computer project B (5%).
Midterm. (25%).
Final exam. (35%).
Computer Project A will be due on Monday, Oct 26, at 8:00pm.
The midterm will be on Thursday, Nov 12, in class.
Computer Project B will be due on Monday, Nov 30, at 8:00pm.
The final exam is Thursday, Dec 10, 3-6pm.

Computer Project A (to be submitted by EMAIL to me by Monday, Oct 26, at 8:00pm):
Design and write an R function which takes as inputs your cards and other variables described in class, and which returns an integer indicating a fold or all-in bet. Your code, once submitted, will be in the public domain and free for others to read and use. Submit your R function to me by email at frederic@stat.ucla.edu .

Computer Project B will be similar to project A, but will take as inputs the variables described in class, and will return an integer indicating whether to fold, call, bet, or raise, and in the latter two cases, how much to bet.

Note: I will give you various examples that you can imitate for your project, but your code must in some way be different from the examples provided.

There will be 4 homework assignments, beginning with HW1 which is due Thurs Oct 1. Homeworks must be handed in at the beginning of class, or may be slipped under my office door (MS 8965) any time before class. Each homework assignment is graded out of 10 points. Homeworks handed in more than 5 minutes after class begins will be given a one-point deduction. Those handed in more than 20 minutes after class begins will be given a two-point deduction. Those submitted more than 60 minutes after class begins will be given a three-point deduction. Homeworks submitted after the end of lecture will not be accepted. Homeworks must be submitted in hard copy, rather than by email or fax.

Rough Outline:
Week 1: Introductory material, gambing addiction, rules of hold'em.
Week 2: Counting problems, combinations, permutations, multiplication rules for counting, axioms of probability.
Week 3: Addition and multiplication rules for probability, simulation, R.
Week 4: Conditional probability, independence, odds ratio, Bayes' rule.
Week 5: Random variables, probability mass functions, distribution functions, densities, expected value, pot odds.
Week 6: Computer project A.
Week 7: Variance, standard deviation, discrete distributions (Bernoulli, binomial, Poisson, geometric, negative binomial, hypergeometric), continuous distributions (uniform, normal, exponential).
Week 8: Midterm. Week 9: Laws of large numbers, central limit theorem, checking and testing results, Markov processes.
Week 10: Computer project B, review.