MTH 452 Mathematical Statistics

Department of Mathematics, U. of Rhode Island

Go To Calendar

             

Go To download Slides




Instructor
Orlando Merino, merino@math.uri.edu, 874-4442, Tyler Hall 220
Term
 Spring 2006
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 (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
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.

MTH 452  Spring 2006 Calendar  

Weekly topics may change if we fall behind schedule.  

day/Month  Events + Evaluation  Section
 planned

Section
covered
Problems                                                 -
 Tu. Jan 24
 Th. Jan 26


5.1, 5.2
5.2, 5.3

p. 316: 1, 3, 6, 8, 9, 12;  
p.322: 14, 15, 21, 23
 Tu. Jan 31
 Th. Feb 2
HW + Quiz

5.3
5.4 (all)

p. 333: 2, 10, 13, 17, 23
p. 344: 3, 5, 9;   p. 349: 14, 15
 Tu. Feb 7
 Th. Feb 9
HW + Quiz

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 14
 Th. Feb 16
HW + Quiz

6.2
6.3

p. 374: 1, 2, 4, 6, 7, 10
p. 380: 1, 2, 4, 9
 Tu. Feb 21
 Th. Feb 23
HW + Quiz

6.4
Neyman-Pearson L.

 Homework (pdf document)
 Tu. Feb 28
 Th. Feb 30
 HW + Quiz
7.2
7.3

7.2.1,
7.3.2, 7.3.8, 7.3.11
 Tu. Mar 7
 Th. Mar 9
HW + Quiz

7.3
7.4
7.5

7.3.16, 7.3.19,
7.4.2, 7.4.13, 7.4.14
7.5.1, 7.5.2, 7.5.12, 7.5.13
 Tu. Mar 14
 Th. Mar 16
       Spring Break


  SPRING BREAK
 Tu. Mar 21
 Th. Mar 23
  HW + Quiz      
  MIDTERM TEST Thursday
9.2, 9.3
TEST

9.2.1, 9.2.4, 9.3.3, 9.3.4
     
 Tu. Mar 28
 Th. Mar 30
HW + Quiz

9.4, 9.5
10.2

 9.4.4,  9.5.3,  9.5.8,  9.5.10
10.2.1, 10.2.2, 10.2.4, 10.2.7
 Tu. Apr 4
 Th. Apr 6
HW + Quiz

10.3
10.4

10.3.1, 10.3.2, 10.3.4, 10.3.5, 10.3.6
10.4.1, 10.4.5, 10.4.6, 10.4.10
 Tu. Apr 11
 Th. Apr 13
HW + Quiz

10.5
11.2

10.5.3, 10.5.4, 10.5.5
11.2.11, 11.2.21, 11.2.29
 Tu. Apr 18
 Th. Apr 20
HW + Quiz

11.3 (up to p.595)
11.3 (p.598-601)
11.4 (p. 606-611)

11.3.1, 11.3.2, 11.3.3, 11.3.5, 11.3.9
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 25
 Th. Apr 27
HW + Quiz

11.5
12.2

11.5.1, 11.5.4, 11.5.7, 11.5.8,
 To be announced



MTH 452  Slides  

 Week / Topics
Screen Version
Print Version
 Week 1 - Sections 5.1, 5.2, 5.3
mth452Sec5.1+5.2+5.3.pdf
mth452Sec5.1+5.2+5.3print.pdf
Week 2 - Sections 5.3, 5.4
mth452Sec5.4.pdf
mth452Sec5.4print.pdf
Week 3 - Sections 5.5, 5.6, 5.7
mth452Sec5.5+5.6+5.7.pdf
mth452Sec5.5+5.6+5.7print.pdf
Week 4 - Sections 6.2+6.3
mth452Sec6.2+6.3.pdf
mth4452Sec6.2+6.3print.pdf
Week 5 - Sections 6.4+6.5
mth452Sec6.4+6.5.pdf
mth452Sec6.4+6.5print.pdf
Week 6 - Sections 7.2, 7.3
mth452Sec7.2.pdf
mth452Sec7.3.pdf
mth452Sec7.2print.pdf
mth452Sec7.3print.pdf
Week 7 - no handouts


Week 8 - Sections 9.2, 9.3
mth452Sec9.2-9.3.pdf
mth452Sec9.2-9.3print.pdf
Week 9 - Sections 9.4, 9.5
mth452Sec9.4-9.5.pdf
mth452Sec9.4-9.5print.pdf





s