MTH 452 Mathematical Statistics

Department of Mathematics, U. of Rhode Island

 Instructor Orlando Merino, merino@math.uri.edu, 874-4442, Tyler Hall 220 Term Spring 2007 Text Introduction to Mathematical Statistics, by R. J. Larsen and M. L. Marx, 4th Edition. Topics Most of chapters 5-12 of the textbook: Estimation Theory, Maximum Likelihood, Cramer-Rao bounds, Hypothesis testing, Type I and Type II errors, point estimates for normal distribution, confidence intervals, chi^2, F, t distributions, Types of data, two sample problems, Regression, analysis of variance. Evaluation Weekly homework (25%), quizzes (25%), one midterm exam (25 %), a comprehensive final exam (25 %) Note: 75% of the final exam will be on sections discussed after the midterm. Date of Midterm Exam: March 15. On the course MTH 452 is an introduction to the mathematics of statistical analysis. It assumes that you have had a course in probability equivalent to MTH 451. You will learn the theoretical basis for statistics and the most important examples of how the fundamental ideas give rise to practical statistical methods. While we will work with data on occasion, the main emphasis will be on the underlying mathematics, with an eye toward understanding the rationale for statistical methods whether they are used in the social sciences, physical sciences, or engineering. Since most statistical methods are based on ideas from probability theory, we will make a lot of use of your knowledge of probability. This course also provides substantial preparation for actuarial science and the actuarial exams. More information on this will be provided upon request. Homework Information HW 1 Problems: Sec 5.2: 1,3,6,8,9,12,15,18,22,24   Homework 1 hints HW 2 Problems: Sec. 5.3: 2,10,13,17,23; Sec 5.4: 3,5,10   Homework 2 hints HW 3 Problems: Sec. 5.4: 17, 20 ; Sec 5.5: 1, 2, 3, 4   Homework 3 hints HW 4 Problems: Sec. 5.6: 1, 3, 5, 8, 9, 10. Due Tuesday.   Homework 4 hints HW 5 Problems: Sec. 6.2: 1, 2, 3, 4, 7, 8, 9 Due Tuesday.   Homework 5 hints HW 6 Problems: Sec. 6.3: 1, 2, 3, 4, 7; Sec. 6.4: 4, 5, 7, 8, 10, 12, 18 Due Tuesday.   Homework 6 hints HW 7 Problems: Sec. 7.4: 8, 10, 12, 13, 19, 21 Due Tuesday.   Homework 7 hints HW 8 Problems: Sec. 7.5: 1a, 2b, 3c, 4a, 6, 9a, 14 and Sec. 9.2: 4, 5, 13   Homework 8 hints HW 9 Problems: 9.2.15, 9.3.1, 9.3.6, 9.4.1, 9.4.2, 9.5.2, 9.5.10   Homework 9 hints HW 10 Problems: 10.2: 1, 2, 4, 7; 10.3: 1, 2, 4, 5, 6   Homework 10 hints HW 11 Problems: 10.4: 1, 5, 6, 10; and 11.2: 11, 20, 26, 30   Homework 11 hints HW 12 Problems (will not be collected): 11.3: 1, 2, 3, 5, 9   Homework 12 hints