Syllabus for the final exam: Probability space, events and set theoretic operations, equally likely events (e.g. birthday problem, matching problem), elementary counting arguments, conditional probability and Bayes' rule, independence, inclusion-exclusion principle, random variables (density, distribution, expectation, variance), familiar distributions (Bernoulli, binomial, geometric, Poisson, Gamma, exponential, normal, uniform), method of indicators, law of large numbers, Chebychev's inequality, properties of expectation and variance, change of variable formula, moment generating functions, central limit theorem and applications, parameter estimation in statistical models, maximum likelihood estimation, asymptotic distribution of MLE, Cramér-Rao lower bound, basics of confidence intervals and hypothesis testing, Student's t, delta method (propagation of error), variance stabilizing transforms, joint densities, conditional densities, multivariate normal distribution.
Instructions about the final:The final exam will be handed out on Friday, November 30, and should be turned in on Monday, December 3, both in class. Please do not consult with any human being except yourself. However, consulting the textbooks and your notes is allowed.
I will hold special office hours from 2 to 4 on Thursday, in case you have any last minute questions.
Practice problems for the final
Solutions to some problems from HW 3 and 4
Homework 1 (due 9/14/2007): Hoel-Port-Stone Chapter 1, ex. 21, 28, 31, 34, 38, 41. Scanned pages
Homework 2 (due 9/28/2007): Hoel-Port-Stone Chapter 2, ex. 7, 11, 21. Chapter 3, ex. 10, 17, 27.
Homework 3 (due 10/10/2007): Hoel-Port-Stone Chapter 4, ex. 15, 17, 24, 29, 30, 32. (Read the passage between ex. 30 and 31 for doing ex. 32.)
Homework 4 (due 10/22/2007): Hoel-Port-Stone Chapter 5, ex. 2, 44. Chapter 7, ex. 34, 35, 43. Chapter 8, ex. 6.
Homework 5 (due 11/9/2007): Click here.
Instructor: Sourav Chatterjee, 333 Evans Hall. Email: sourav@stat.berkeley.edu
Instructor office hours: Mon 4-6 at the instructor's office. Also by appointment.
Class schedule: MWF 12-1 in 0213 Wheeler.
GSI: Arnab Sen, 437 Evans Hall. Email: arnab@stat.berkeley.edu
GSI office hours: T 11-12, Th 10-11 at 307 Evans.
Prerequisites: Two years of calculus and one semester of linear algebra.
Midterm: Wednesday, October 24. In class.
Final exam: To be handed out on Friday, November 30, and turned in on Monday, December 3, in class.
Grading: 40% on final, 30% on midterm, 30% on homeworks.
Letter grade: Based on your performance in comparison to others (that is, "graded on the curve").
Texts:
(1) Introduction to Probability Theory
by P. G. Hoel, S. C. Port and C. J. Stone.
(2) Mathematical Statistics: Basic ideas and selected topics
by P. J. Bickel and K. A. Doksum.
Link to official course website.
Link to instructor's homepage.