Instructor: L. Pakula, Tyler 201, X4519, pakula@math.uri.edu
Office Hours: M-TH 10-11 or by appointment
Text: Miller & Miller, Freund's Mathematical Statistics , 7th Edition
Time: T-Th 12:30-1:45
Room: Tyler 109 (NOTE ROOM CHANGE)
NOTE: Final Exam is May 8 at 11:30 AM in Tyler 109. A study guide can be found below. Project is due at that time as well. Some hints can be found below. There are new links to HW solutions in the syllabus table.
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.
In keeping with recent trends, we will do some computing, using Maple, Excel, or other programs.
This course also provides substantial preparation for actuarial science and the actuarial exams. More information on this will be provided later.
Here is a small Excel worksheet with which you can quickly find values
for normal, chi-square and t distributions -- better than tables.
If you have Excel on your computer
the sheet should open when you click on it. You can save it, of course,
but your system might tell you that it's written in an older version of
Excel (because it is!).
Statistical
distribution values
The following is a very nice little statistical calculator that you can use to try out some of the methods we study.
The course will cover topics from chapters 6,7,8,10,11,12,13 and 14 in the text as well as some additional material. Problems will be assigned as we go and will be posted here. Some problems will be assigned as homework and discussed at the next class meeting. There will be some review problem sets to hand in to be graded and a small project at the end of the semester. There will be occasional quizzes, too, which will be announced in advance.
There will be a mid-term exam in class (date to be announced later) and a final exam during the regular final exam period.
Grades will be composed as follows:
Midterm 25%
Final Exam 35%
HW, quizzes and project 40%
| Date | Reading | Exercises in textbook | Handouts/Links |
| Jan 24 | 7.1, 7.2 | 7.1, 7.2 | |
| Jan 29 | 7.3 | 7.3,7.11,7.16,7.19,7.20 | |
| Jan 31 | 7.4 | 7.18, 7.36 | Dist. Families , Joint dens. example from class, Some hw solutions , More hw solutions |
| Feb 5 | 7.5 | 7.43, 7.45 | |
| Feb 7 | 8.1,8.2,8.4 | 8.2,8.3,8.16,8.17 | |
| Feb 12 | 8.4,8.5 | 8.18, 8.19,8.20, 8.22, 8.23 | |
| Feb 14 | 8.7, 10.2 | (NO 8.41!),8.44, 8.67,8.77,8.79,10.1 Problems to Hand in 2/19: 8.18,8.19,8.20,8.46,8.67 |
HW solutions |
| Feb 19 | 10.3 | 10.5,10.6, 10.15,10.17 | |
| Feb 26 | 10.4-10.6 | 10.21,10.22,10.31,10.36, 10.42,10.49 | Class note on efficiency | Feb 28 | 10.7-10.8 | 10.51,10.53,10.61 | HW solutions | Mar 4 | 11.1-11.2 | 11.1,11.10 | Mar 6 | 11.3-11.4 | 11.4, 11.5, 11.6, 11.9 | 11.4 | 11.12, 11.13,11.43 | Mar 25 | 11.6-7, 10.9 | 10.74, 10.93 (use 6.29 without proof) | Solutions | Mar 27 | 12.1,12.2 | Apr 1 | 12.4 | 12.7,12.10,12.15, 12.11 | HW solutions (new) | Apr 8 | 12.5 | Hyp.test for Bin(n,p) h.o. Hyp.test for Exp(theta) h.o. | April 10 | 12.6, 13.1 | 12.19,12.20, 12.21 | April 17 | 13.2-13.4 | 13.19, 13.20, 13.21,13.25, 13.26, 13.27, 13.33, 13.47 | HW solutions | April 22 | 14.1, 14.2 | Notes on regression (expanded) Bivariate normal pictures | April 24 | 14.1, 14.2 | 14.11, 14.13,14.17, 14.41,14,42 | Hand in 4/29: 13.25,13.26, 14.13, 14.17, 14.41 | April 29 | 14.3, 14.4 | HW solutions I |
Data sets for project (as text files)
DataSet1
DataSet2
DataSet3
DataSet4
Data sets for project (as Excel files)