Class meetings: MWF 10:30-11:20 Lowe 105
Instructor: Michael Perlman, Department of Statistics
Office: B310 Padelford Hall
Phone: (206) 543-7735
Email: michael@stat.washington.edu
Office hours: MWF after class (11:20-??) or by appointment.
Problem sessions: TBA (generally one day before homework is due).

We will cover the mathematical (not philosophical) foundations of probability theory.

The basic vocabulary of probability theory includes: random experiment, sample = outcome space (discrete and continuous cases, event, probability measure = distribution, random variable, probability mass function (discrete), probability density function (continuous), cumulative distribution function, independent events, independent random variables, conditional probability and Bayes' Formula, conditional distribution, expected value = mean value and conditional expectation, variance, standard deviation, moments, random vectors, joint distribution, covariance and correlation.

Special distributions include the Bernoulli, binomial, geometric, negative binomial, Poisson, hypergeometric, uniform, normal = Gaussian, exponential, gamma, and bivariate/multivariate versions of some of these, especially the multinomial and multinormal.

Basic results include formulas for the distribution of transformations = functions of random variables and random vectors, the Law of Large Numbers, and the Central Limit Theorem = normal approximation.

We shall also discuss examples of stochastic processes, which consist of (countably or uncountably) infinite sequences of random variables, such as the results of an infinite sequence of coin tosses, and study their limiting behavior. A more detailed treatment of stochastic processes is presented in 396.

NOTE: 394-5 will be presented as a CONNECTED SEQUENCE. Thus, some key topics (for example, expectation, joint distributions) will be introduced in 394 but not fully developed until 395. In order to fully master these topics, it is important to take BOTH 394-5 in sequence. Also, different instructors may structure the sequence differently, so it is highly recommended that you remain in the SAME SECTION for 394 and 395.

"A First Course in Probability" (7th ed.) by S. Ross. This is a lively text that covers the basic ideas of probability theory including those needed in mathematical statistics. Theoretical concepts are introduced via interesting concrete examples. (However, some of the examples are introduced too early, and more properly belong in 396. We will simply skip such examples for now.)

In 394 I will begin my lectures with the basics of probability theory in Chapter 2. However, your first assignment is to review Chapter 1, which treats elementary counting methods.

In 394 I expect to cover Chapters 2-5 plus portions of 6 and 7, then the remainder of Ross in 395. You are encouraged to read ahead. I will not be able to cover every topic in Ross in lectures, and conversely, I may cover some topics in lectures that are not treated in Ross. Furthermore, my lectures may not always conform exactly to the order of material in the textbook. (For example, the concept of expected value of a random variable, which does not appear until Chapter 4, will be introduced earlier in an informal manner.)

I have also prepared a set of class notes (designated MDP). These will be available in the UW bookstore, alongside Ross. Some of my lectures, as well as some homework problems, will come from these notes

You will be responsible for all material in my lectures, assigned reading, homework, and exams, including supplementary handouts if any.

"An Introduction to Probability Theory and Its Applications" (Vol. I) by W. Feller. This is a classic introductory text, written by a master. Only discrete probability spaces are treated, limiting its use as a textbook, but Feller shows us how to "think probabilistically", with many interesting and important examples.

"Elementary Probability Theory with Stochastic Processes" by K. Chung.

"Introduction to Probability Theory" by D. Hoel, S. Port, and C. Stone.

Copies of these books, plus Ross, are on reserve in the Math Research Library, Padelford Hall, 3rd Floor.

MATH 126, MATH 129, or MATH 136. Recommended: MATH 324 or 327.

MATH/STAT 394-5 is an introductory sequence in probability, but not in mathematics. Calculus (including multiple integrals), elementary combinatorics, and some linear algebra will be used. Two math self-diagnostic exams can be found on the course home page - these indicates the math level and content that will be assumed for 394-5.

HW assignments will be given weekly (days will vary). Please write neatly and legibly! Please write your NAME clearly on all HW, and staple all sheets together. Late HW will be acknowledged but not graded.

The problems and exercises in Ross are generally of good quality. Not all will be assigned formally, but you are strongly encouraged to read and attempt as many as possible. (Note that complete solutions to the "self-test problems and exercises" are presented in Appendix B.) Most homework problems will come from Ross, but occasionally I will assign some supplementary ones.

Each week I will hold an extra problem session, usually one day before the next homework assignment is due. (Time and place to be determined by the availablility of most students.) This will be of most value to you if you have already thought hard and carefully about the homework problems, solving as many of them as you can, then ask me to help clarify any remaining uncertainties. For obvious reasons (e.g., exam performance), this will be of NEGATIVE value to you if you do not think about the problems in advance and, instead, rely primarily on my thinking, not your own.

I will also be happy to respond to any questions by email, time permitting. I may send my reply to the entire class if it is of general interest.

One-hour Midterm Exam and comprehensive Final Exam. Exams are open book and notes.

394/5: Homework 30%, Midterm 20%, Final 50%