Syllabus.  
Statistics 100a:  Introduction to Probability.<br>
Prof. Rick Paik Schoenberg. <br>

Winter 2015. <br><br>

Lectures:  TTh 11am - 1215pm, Young CS24.
<br><br>

Office Hours:  Tue 10-11am, Math-Sciences 8983.<br><br>

Email:  frederic@stat.ucla.edu<br><br>

Course webpage:  <a href="http://www.stat.ucla.edu/~frederic/100a/w15">
http://www.stat.ucla.edu/~frederic/100a/w15 </a><br><br>

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

Errors in the textbook: <a 
href="http://www.stat.ucla.edu/~frederic/errors.html">
http://www.stat.ucla.edu/~frederic/errors.html </a><br><br>

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. <br><br>

Grading: <br>
Homework (23%).<br>
Team computer project (2%). <br>
Exam 1. (25%).<br>
Exam 2. (25%).<br>
Exam 3. (25%).<br><br>

The computer project will be due on Tue Mar 3 8:00pm.<br>
Exam 1 will be on Thu, Feb 5.<br>
Exam 2 will be on Tue, Mar 3.
Exam 3 will be on the last class, Mar 12.<br>
There will be no final exam after Mar 12.<br>

The exams will be open book and open note, 
plus each student should bring a calculator and a pen or pencil. 
Computers are not allowed for the exams.<br><br>

Computer Project (to be submitted by EMAIL to me by Tue Mar 3 8pm):<br>
 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 . <br><br>
 
  Note: I will randomly assign you to teams in week 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.
 <br><br>

There will be 3 homework assignments, beginning with HW1 which is due
Thu Jan 29 at the very beginning of class.
Homeworks must be handed in at the beginning of lecture, or earlier by 
sliding them under my office door. 
Each homework assignment 
is graded out of 10 points. 
Homeworks handed in more than 5 minutes after lecture 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 submitted more than 15 minutes after class
begins will be given a 3 point deduction. After 20 minutes into class, 
further homeworks will not be accepted.
Homeworks must be submitted in hard copy, rather than by email or fax. <br><br>

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. 
<br><br>

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