MATH/STAT 394: Probability I

Winter Quarter 2000

Syllabus (last updated: 1/20/2000)

Course personnel:

• Professor: Jon A. Wellner
• B320 Padelford Hall
• Phone: 543-6207
• Office hours: 1:00 - 3:00 MWF; or by appointment

Administrative Information:

• Time(s): MWF 8:30 - 9:20
  
• Place: Raitt 121 (moved from Smith 305!)

Prerequisites:

• 2.0 in Math 126 or 2.0 in Math 136.
  Recommended: Math 324 or Math 327.
  
• Be sure you can handle the math in Appendix A of Kelly!
• MATH/STAT 394 is an introductory sequence. If you have already had a math course in probability, you should not be taking 394.

Required Texts:

• Introduction to Probability, by Douglas G. Kelly, Macmillan, 1994. Required. (Requested 38 times, Math Research Library, Winter 2000.)

Supplemental texts:

• Feller, Introduction to Probability Theory and Its Applications , Vol. I. 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. (Requested 21 times, Winter 2000.)
• Ross, A First Course in Probability. This is a more modern text than Feller, also with interesting examples. (Requested 27 times, Winter 2000.)
• Durrett. The Essentials of Probability. A thin but modern textbook; mathematical style exercises. (Requested 0 times, Winter 2000.)
• Hoel, Port, and Stone, Introduction to Probability Theory. (Requested 19 times, Winter 2000.)
• Chung, Elementary Probability Theory with Stochastic Processes. (Requested 0 times, Winter 2000.)

Grading:

• Homework: 30%
• Midterm: 35%; (Monday, February 7).
• Final: 35%
  (Scheduled time & date: 8:30 - 10:20, Tuesday, March 14).

Homework:

• Weekly HW assignments due each Wednesday in class at the beginning of the hour.
  
• Please write neatly and legibly!
  
• We will try to return graded HW to you promptly.
• Please write your NAME clearly on all HW, and please staple all sheets together.
• Late HW will be acknowledged, but not graded.
• You may discuss homework problems with you classmates, either in person or by e-mail, but what you hand in must be your own work.
• After HW is turned in on Wednesday mornings, Solutions will be posted on the course web-page.

Lectures and Handouts:

We shall 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 uncoutably) infinite squences of random variables, such as the results of an infinite sequence of coin tosses, and study their limiting behavior.}

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