MATH 3236 Statistical Theory

Spring 2020

MW 3:00 - 4:15 Skiles 169

Instructor: Federico Bonetto

Office Hours: MW 2:00 - 3:00, Skiles 133b

The course will introduce the basic notion of statistical theory. The focus will be both on mathematical derivation and on the discussion of applications. The course is meant to be the secons of a two courses series on Probability and Statistics.

The text that will be used is:

Morris DeGroot & Mark Schervish, Probability and Statistics, 4th ed., Addison-Wesley

The syllabus can be found here. This is only the second time this class is offered so the exact syllabus may change, mostly toward the end of the class. Any change will be discussed in class.

There will be two midterm.

The exercise listed are for HW collection. I will collect them every othewr week and grade 2 or 3 exercises among the one assigned.

The final grade will be based on the following rules: 45% final, 40% midterms, 15% HW. Curving will be done on the final result. The possibility of personal project will be discussed later during the class.

The first midterm is tentatively scheduled for Wednesday February 19 and the second on Wednesday March 11.

First week.

Material covered: Introduction and basic review of Probability Theory. Chapter 6.1, 6.2.

Exercises: Chapter 6.2 ex n. 3, 7, 15

Second week.

Material covered: Chapter 6.3 and 7.1 with example 4.7.8 p. 261

Exercises: Chapter 6.3 ex n. 4, 10

Solution set for the first HW.

Third week.

Material covered: Chapter 5 sections 5.7 and 5.8 to 2.5.

Exercises: Chapter 5.7: 4, 10, 19, Chapter 5.8: 5, 8

Fourth week.

Material covered: Chapter 7 section 7.2 and 7.3.

Exercises: Chapter 7.2: 3, 10, Chapter 7.3: 7,8, 12

Solution set for the second HW.

Fifth week.

Material covered: Chapter 7 section 7.4 and 7.5.

Exercises: Chapter 7.4: 6, 12, 13, Chapter 7.5: 5, 9, 10

Sixth week.

Material covered: Chapter 7 section 7.6 and 7.7 and 6.6 from R.V. Hoggs and E.A. Tanis "Probability ans Statistical Inference".

Exercises: Chapter 7.6: 9, 12, 23, Chapter 7.7: 7, 9

Here is the take home Midterm 1 (and the tex file for your convenience). It is based on the Pareto distribution and it is an attempt to run the concepts we have learned in the class on a real example. The midterm is due on Tuesday 2/25 at 8pm. If you submit it electronically, please print and sign the cover page as an aknoledgement that you have worked on your own.

Here are the solution for the take home midterm.

As quoted in the test research on the relations among Pareto distribution, wealth distribution and economic inequality is active. Here a couple of example: On a Kinetic Model for a Simple Market Economy or Statistical Equilibrium Wealth Distribution in a Exchange Economy with Stochastic Preference . This is an area of research I'm quite interested in. I'll be more than happy to discuss with you if you find the question interestin

Sevenh-Tenth week.

Material covered: Chapter 8 section 8.1 to 8.7

Exercises: Chapter 8.1: 2, 9, Chapter 8.2: 4, 7, 10 Chapter 8.3: 5, 7 Chapter 8.4: 3, Chapter 8.5: 1, 4, 7 Chapter 8.6: 5, 8, 10, 11