Syllabus. Statistics 100a: Introduction to Probability.
Prof. Rick Paik Schoenberg.
Fall 2017.

Lectures: TTh 11-12:20 Bunche 2209a.

Office Hours: Tue 12:20-1pm, Math-Science 8965.

Email: frederic@stat.ucla.edu

Course webpage: http://www.stat.ucla.edu/~frederic/100a/F17

Textbook: Schoenberg, F. (2016). An Introduction to Probability with Texas Hold'em Examples, 2nd ed. Taylor and Francis, New York.

Errors in the 1st edition of 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 (15%).
Team computer project (5%).
Exam 1. (25%).
Exam 2. (25%).
Exam 3. (30%).

Exam 1 will be on Tue, Nov 7.
Exam 2 will be on Tue, Nov21.
The computer project will be due on Sat Dec2 8:00pm.
Exam 3 will be on the last class, Thu Dec7.
For all exams, students will be allowed to use the textbook and any paper notes. Please bring a calculator and either a pen or pencil for all exams. Computers, phones, tablets, and anything that can text or email is not allowed for the exams.

Gradegrubbing procedure: if you would like a question (or more than one question) reevaluated, submit your exam or homework and a WRITTEN explanation of why you think you deserve more points and how many more points you think you deserve to your TA. The TA will then give it to me, and I will consider it, and then give it back to the TA to give back to you.

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 or 3. 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, due at the very beginning of class. Homeworks must be done independently of other students. Your hw may be handed in at the beginning of class, or may be slipped under my office door 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 10 minutes after class begins will be given a two point deduction. Those handed in more than 20 minutes after class begins will be given a three point deduction. Those submitted more than 40 minutes after class begins will be given a four 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 generally 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.

I am almost always open to questions, but one question I would like you not to ask me is "What did we do in class?" If you miss class, please get caught up on the notes from a fellow classmate.

Rough Outline:
Weeks 1-2: Introductory material, gambing addiction, rules of hold'em, counting problems, combinations, permutations, multiplication rules for counting, axioms of probability.
Weeks 3-4: Addition and multiplication rules for probability, simulation, R, conditional probability, independence, odds ratios, Bayes' rule, random variables.
Weeks 5-6: Exam 1, 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).
Weeks 7-8: Laws of large numbers, central limit theorem, checking and testing results, exam 2.
Weeks 9-10: Random walks, computer project, moment generating functions, review, exam 3.