Syllabus. Statistics 100a: Introduction to Probability.
Prof. Rick Paik Schoenberg.
Summer 2015.

Lectures: TTh 10am - 1150am, Young CS24.

Office Hours: Tue 925-955am, Math-Science 8983.

Email: frederic@stat.ucla.edu

Course webpage: http://www.stat.ucla.edu/~frederic/100a/S15

Textbook: Schoenberg, F. (2011). An Introduction to Probability with Texas Hold'em Examples. Taylor and Francis, New York.

Errors in the textbook: http://www.stat.ucla.edu/~frederic/errors.html

Description: Exploration of the main topics in introductory probability theory, especially discrete probability problems, that are useful in a wide variety of scientific applications. Topics include conditional probability, expectation, combinatorics, laws of large numbers, central limit theorem, Bayes theorem, univariate distributions, conditional expectation, moment generating functions, and random walks. We will also examine computer simulation in depth and discuss 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:
Homework (12%).
Team computer project (3%).
Exam 1. (20%).
Exam 2. (20%).
Exam 3. (45%).

Exam 1 will be Jul 9.
The computer project will be due on Sun Jul 27, 8pm.
Exam 2 will be Jul 21.
Exam 3 will be Jul 30.
For Exam 1, students can use the textbook and one 8.5 x 11 double sided page of notes, plus any calculator and a pen or pencil. For Exams 2 and 3, students can use the textbook and two 8.5 x 11 double sided pages of notes, plus a calculator and a pen or pencil. Computers are not allowed for the exams.

Computer Project (to be submitted by EMAIL to me):
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 .

Note: I will randomly assign you to teams in week 2. 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 3 homework assignments, beginning with HW1 which is due Jun 30 at the very beginning of class. Homeworks must be handed in at the beginning of class, or may be slipped under my office door (MS 8983) 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 40 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.

There will be no make-up exams. Students who are unable to take an exam must consult with the instructor in advance. Those who cannot take an exam because of an emergency must meet with the instructor to make special arrangements. Students with learning disabilities must consult with the instructor by the 4th lecture if special arrangements are required. Cheating will absolutely not be tolerated. All homework and exam problems are to be solved independently. Any students caught cheating will face appropriate University disciplinary action.

Rough Outline:
Week 1: Introductory material, gambing addiction, rules of hold'em, counting problems, combinations, permutations, multiplication rules for counting, axioms of probability.
Week 2: Addition and multiplication rules for probability, simulation, R, conditional probability, independence, odds ratios, Bayes' rule, random variables.
Week 3: Probability mass functions, distribution functions, densities, expected value, pot odds, variance, standard deviation, discrete distributions (Bernoulli, binomial, Poisson, geometric, negative binomial, hypergeometric), continuous distributions (uniform, normal, exponential).
Week 4: Laws of large numbers, central limit theorem, checking and testing results, random walks.
Week 5: Computer project, moment generating functions, more about random walks, review.
Week 6: Review and final exam.