# Probability Theory with Applications

 Instructor: David Pollard Webpage: http://www.stat.yale.edu/~pollard/Courses/241.fall2011 When: MWF 9:25-10:15 Where: WLH 208 Final Exam: Saturday 17 December at 9:00am in room 220 Dunham Laboratory Office hours: Wednesday 12:38-2:00 and 3:00-5:00. Tuesday 12:00-1:00, over lunch at Silliman College. Questions are also welcome immediately after each lecture. TA: Sabayasachi Chatterjee (Office hour: Tuesday 1:30-2:30 in basement, 24 Hillhouse) Other help: Residential College Math & Science Tutoring Program 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. Grading: 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 2011 notes will be similar, but not identical, to the 2005 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 2005 for a rough guide. In fact, I will be re-editing then posting those notes as the semester progresses.

DBP 26 Aug 2011