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

Lectures: Mondays and Wednesdays, 1pm - 2:50pm, Boelter 5264.

Office Hours: Mondays, 3:00 to 3:50 pm, Math-Science 8965.

Email: frederic@stat.ucla.edu

Course webpage: http://www.stat.ucla.edu/~frederic/35b/sum09

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 (20%).
Computer project A (10%).
Computer project B (15%).
Midterm. (20%).
Final exam. (30%).
Computer Project A will be due on Saturday, Aug 15, at 8:00pm.
The midterm will be on Monday, Aug 24, in class.
Computer Project B will be due on Saturday, Aug 29, at 8:00pm.
The final exam is Wednesday, Sept 2, in class.

Computer Project A (to be submitted by EMAIL to me by Saturday, Aug 15, 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 Monday Aug 10. 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:
Day 1: Introductory material. Counting problems, combinations, permutations, multiplication rules for counting, axioms of probability, gambing addiction, rules of hold'em.
Day 2: Addition and multiplication rules for probability, simulation, R.
Day 3: Conditional probability, independence, odds ratio, Bayes' rule.
Day 4: Random variables, probability mass functions, distribution functions, densities, expected value, pot odds.
Day 5: Computer project A.
Day 6: Variance, standard deviation, discrete distributions (Bernoulli, binomial, Poisson, geometric, negative binomial, hypergeometric), continuous distributions (uniform, normal, exponential).
Day 7: Midterm. Day 8: Laws of large numbers, central limit theorem, checking and testing results, Markov processes.
Day 9: Computer project B, review.
Day 10: Final exam.