Northeastern University, Mathematics Department
Mathematical Statistics MTH 1390
Spring 2000, Class Meetings:Tu.-Fr. 8-9.05, W.,1.35-2.40;
Instructor: Prof. Michael Malyutov
office : 545 Lake, phone: x5650, e-mail: MLTV@neu.edu
ofiice hours: Monday, Friday, 3-4 p.m., or by appointment.
Syllabus
Textbook: "An Introduction to Mathematical Statistics and its Applications"
by R. Larsen and M. Marx, second edition, Prentice Hall, Englewood, 1986.
The instructor has a partial copy of the revised third edition due in May.
It was sent by publishers to use some of the new material in this class.
The goal of the course is to introduce major concepts and study elementary parameter estimation and testing statistical hypotheses techniques based on Calculus. An attempt to introduce simple applications of the package SPSS for statistical computations may be made for interested students.
Although Probability MTH 1387 is formally a prerequisite, our practice dictates to deal with those who have never taken it (the last category sometimes includes Industrial and Mechanical Engineering majors). By this reason we start with a problem of margin-of-error, which shows the statistics/probability contrast and reviews the relevant of MTH 1387. The rest relevant of MTH 1387 will be reviewed and used progressively.
Outline
Estimation
1. Review, margin of error:................................................................4.1, 4.3, 5.10.
2. Estimation, mean square error.......................................................5.1-5.5
3. Maximum likelihood, method of moments...................................5.8
4. Confidence intervals......................................................................5.9-5.10
Testing
1. Philosophy of testing: type 1, type 2 errors...................................6.1-6.3
2. Neyman-Pearson lemma, Likelihood Ratio tests..........................6.4
3. P-value, examples.........................................................................6.3
Cookbook Testing and Normal Distribution
1. Facts about Normals.....................................................................7.3
2. One-sample t-test..........................................................................7.7
3. Two-sample t-test.........................................................................8.2
4. F-test.............................................................................................8.3
5. Confidence intervals for two samples..........................................8.5
Some items may be dropped, some additional material may be added if time permits.
Weekly assignments are 20%. Two best of up to four open book or take home tests is another 40%. The final is 40%.
Notice: It is the student’s responsibility to be aware of what happens in the classroom, including announcements of possible test date changes, adjustments to the syllabus which may occur etc.
Assignments
1.(sections 5.1-5.5); p. 237:1,2(optional); p. 241-242:4,7,9,10; p. 247:3,5.
2. (section 5.8); p.266:2,3,4,5; p. 271: 12, 13, 15.
3. (sections 5.9, 5.10, 6.1, 6.2); p. 280:2,3, p. 282:6,7; p. 291: 2c, 3.
4. (sections 6.1-6.4); p.295:5,7; p.298: 8,9; p. 300: 1,2; p. 304: 3,5, 10.
5. (sections 7.3, 7.4, 8.1, 8.2) p. 325:3; p. 352: 3,7; p. 363:1; p. 369:3,4,6.
6. (sections 8.3- 8.5) p.369:4,9; p. 383: 4; p.390: 1,10