Statistics 241/541, Math 241 (fall 2014)

Probability Theory with Applications

Revised 20 Sept 2014

Instructor: David Pollard
When: MWF 9:25-10:15
Where: WLH 208
Office hours: Wednesday 4:00-5:30, in main classroom of 24 Hillhouse.
Questions are also welcome immediately after each lecture.
TAs: Yu Lu, Ye Zhang, Derek Feng
Office hours: Tues 7:00-8:00; Thurs 3:00-4:00 (main classroom, 24HH)
Final exam: According to YCPS, Stat 241/541 is a member of group (32), whose exams start at 2p.m. on Friday 12 December. Place: DAVIES
Other: courses taught by DP in previous years
Short description: A first course in probability theory: probability spaces, random variables, expectations and probabilities, conditional probability, independence, some discrete and continuous distributions, central limit theorem, law of large numbers. After or concurrent with Mathematics 120a or b or equivalents.
  • The weekly homework (due each Friday) will make up 50% of the final grade, with the other 50% coming from the final exam.
  • No late homeworks accepted without Dean's note. No sheet will be accepted after solutions are posted on web.
  • Students must clearly acknowledge any help received with the homework.
  • Students who wish to work in teams (no more than 2 to a team) should submit a single solution set. Each member of a team will be expected to understand the team's solutions sufficiently well to explain the reasoning at the blackboard. Occasional meetings with DP might be arranged.
  • To get some idea of progress, see the boxplots of homework and midterm scores. See the final plot from 2005 for insights into how I decide how much a homework sheet should be worth.
Text: Detailed notes (in Adobe Acrobat pdf format) will be available for free from this WWW site. The 2014 notes will be similar, but not identical, to the 2011 notes. There is no prescribed text, but you might find some of the supplementary references helpful.
Topics: Probability theory gives a systematic method for describing randomness and uncertainty. This course will explain the rules for manipulating random variables, probabilities, and expectations, with emphasis on the role of conditioning. The theory will be presented and motivated through a sequence of applications, ranging from the (traditional, boring) calculation of probabilities for card games to (more involved, more interesting) stochastic models.

The coin tossing model will generate the standard discrete distributions: Binomial, Poisson, geometric, negative binomial. The Poisson process, the continuous time analog of coin tossing, will generate the standard continuous distributions: exponential and gamma.

Normal approximations and calculations related to the multivariate normal distribution will exercise the multivariable calculus skills of the class (or provide a crash course in multiple integrals).

Applications to include topics like: Markov chains; the probability theory of games, gambling, and insurance; coding theory; queueing theory; branching processes; geometric probability and stereology; (maybe) analysis of algorithms.

The coverage will be similar to, but not exactly the same as, what I have done in previous years. See the notes for 2011 for a rough guide. In fact, I will be re-editing then posting those notes as the semester progresses.

You will be expected to know some Calculus, although past experience has shown that I need to refresh some minds when using multivariate integrals. Look at chapters 11, 12, and 13 in the 2011 notes for an idea of how I will proceed.

Other: Miscellaneous helpful materials.