# 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 2005 Text Introduction to Mathematical Statistics, by R. J. Larsen and M. L. Marx, 3rd Edition, Prentice Hall, ISBN: 0 13 922303 7 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 (20%), quizzes (20%), one midterm exam (25 %), a comprehensive final exam (35 %) Note: 75% of the final exam will be on sections discussed after the midterm 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. We will do some computing, using Maple, Excel, or other software. This course also provides substantial preparation for actuarial science and the actuarial exams. More information on this will be provided later.

## MTH 452  Spring 2005 Calendar

Weekly topics may change if we fall behind schedule.
Assigned problems will appear in this page as soon as they are selected.

 day/Month Events + Evaluation Section planned Section  covered Problems                                                 - Tu. Jan 18  Th. Jan 20 5.2   5.3 5.2 5.2, 5.3 p. 316: 1, 3, 6, 8, 9, 12;   p.322: 14, 15, 21, 23 Tu. Jan 25  Th. Jan 27 HW + Quiz 5.2 5.3 5.4 5.3 5.4 (all) p. 333: 2, 10, 13, 17, 23 p. 344: 3, 5, 9;   p. 349: 14, 15 Tu. Feb 1  Th. Feb 3 HW + Quiz 5.3- 5.4 5.4   5.5 5.5 5.6 5.7 p. 353: 2, 3, 4, 5 p. 356: 2, 3;  p. 358: 6, 8, 10 p. 361: 4 (there is a hint for #4) Tu. Feb 8  Th. Feb 10 HW + Quiz 5.4-5.5 6.2   6.3 6.2 6.3 p. 374: 1, 2, 4, 6, 7, 10 p. 380: 1, 2, 4, 9 Tu. Feb 15  Th. Feb 17 HW + Quiz 6.2-6.3 6.4   6.5 6.4 Neyman-Pearson L. Homework (pdf document) Tu. Feb 22  Th. Feb 24 Tuesday classes don't meet  HW + Quiz 6.4-6.5 ----   7.2 --- 7.2 Tu. Mar 1  Th. Mar 3 HW + Quiz 7.2 7.3   7.4 7.3 7.3-7.4 7.2.1, 7.3.2, 7.3.8, 7.3.11 7.3.16, 7.3.19, 7.4.2, 7.4.13, 7.4.14 Tu. Mar 8  Th. Mar 11 HW + Quiz  7.3-7.4 Thursday Mar 11-Midterm Test 7.5  Test Mar 14-18 Spring Break Spring Break Tu. Mar 22  Th. Mar 23 HW 7.5 9.2   9.3 9.2, 9.3 9.4, 9.5 7.5.1, 7.5.2, 9.2.1, 9.2.4, 9.3.3, 9.3.4 9.4.4,  9.5.3,  9.5.8,  9.5.10 Tu. Mar 29  Th. Mar 31 HW + Quiz 9.2-9.3 9.4   9.5 10.2 10.3 10.2.1, 10.2.2, 10.2.4, 10.2.7 10.3.1, 10.3.2, 10.3.4, 10.3.5, 10.3.6 Tu. Apr 5  Th. Apr 7 HW + Quiz 9.4-9.5 10.2  10.3 10.4 10.5 10.4.1, 10.4.5, 10.4.6, 10.4.10 10.5.3, 10.5.4, 10.5.5 Tu. Apr 12  Th. Apr 14 HW + Quiz 10.2-10.3 10.4  10.5 11.2 11.3 (up to p.595) 11.2.11, 11.2.21, 11.2.29 11.3.1, 11.3.2, 11.3.3, 11.3.5, 11.3.9 Tu. Apr 19  Th. Apr 21 HW + Quiz 10.4-10.5 11.2  11.3 11.3 (p.598-601) 11.4 (p. 606-611) 11.3.16, 11.3.18, 11.3.19, 11.3.25 11.4.1, 11.4.2, 11.4.7, 11.4.8 Tu. Apr 26  Th. Apr 28 HW + Quiz 11.2-11.3 11.4  11.5 11.4 (p. 612-617) 11.5 11.4.15, 11.4.18, 11.5.1, 11.5.4, 11.5.7, 11.5.8, plus problem assigned in class. Tu. May 3  Th. May 5 HW + Quiz  11.4-11.5 12.2  14.2 Tu. May 10 HW + Quiz  12.2, 14.2 Last day of class Tuesday May 10 14.3