| 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. |
| 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 |