### Math 4056 Mathematical Statistics

Time and place: MWF 09:40-10:30, Lockett 240

Textbook: Casella and Berger: Statistical Inference 2nd ed. (This book is available from on-line dealers at a reasonable price.)

Goal: This course deals with the mathematical principles that underlie and justify the most common basic techniques of statistical inference.  The focus is not on the development and use of techniques for dealing with complex statistical problems, but on understanding the most commonly used statistical methods clearly and rigorously.

Grading: Homework 25%.  Friday quizzes 25%.  Midterm and final 50%.

week mm/dd D Topic Assignment Notes/resources

## 1

08/23 M Introduction   Announcements
Presentation (needs Mathematica)
08/25 W Probability review I Read: p. 27-29, p. 34-37, p.86, p. 89, p. 92, p. 102, Sec. 2.2.
Hand in 08/30: (p. 76) 2.4, 2.13, 2.15, 2.20, compute the mgf of a normal(0,1) r.v.
copy of exercises (from text)
08/27 F Quiz (binomial dist.); Probability review II:
Moment generating functions.
Read: Sec. 2.3, pages 182-184 (independence).
Hand in 08/30:
(p. 80) 2.33
notes (Philos. Intro. to Stat. Inf.)

## 2

08/30 M Sampling statistics   notes
09/01 W Sample mean and variance Hand in 09/08: problem in notes. notes
09/03 F Sampling the normal, I. Sums and averages of independent normal variables Hand in 09/08: xeroxed problems: 26, 32, 34; find and do the one other of the problems from 26-36 that is directly related to the new material of today. Read: section 5.2. quiz
notes

## 3

09/06 M Holiday --- ---
09/08 W Sampling the normal, II. Sample variance. Hand in 09/15 (revised date): The problems in the lecture notes for 09/08. notes
09/10 F Change of variables and transformations of random variables. Hand in 09/15: 4.20 (page 194) quiz
notes

## 4

09/13 M Sampling the normal, III. Proofs concluded. Hand in 09/17: 5.6 (page 256). Read: 5.3. see notes from 09/08
09/15 W The gamma and chi-squared distributions Hand in 09/20: the problems in the notes. notes
09/17 F Student's t and Snedecor's F Hand in 09/22: the problems in the notes quiz
notes

## 5

09/20 M Sufficient statistics I   notes
09/22 W Sufficient statistics II Hand in 09/27: problems in notes notes
09/24 F Review Hand in 09/27: problem 6.7 (page 300)
quiz
wikipedia on sufficiency

## 6

09/27 M Liklihood and the MLE -- notes
09/29 W MLE may be biased See notes notes
10/01 F Poisson MLE We discussed the quiz quiz with commentary

## 7

10/04 M Mean Squared Error Homework (9/24) due date revised;
Get Homework Hints.
notes
10/06 W Misc. Problems
10/08 F Homework review   Notes to Review for Midterm

## 8

10/11 M Review for Midterm
10/13 W Midterm Exam Students will receive a "curved score" (i.e., more points) if they work the exam problems at home and hand them in on Friday.
10/15 F discussion of exam

## 9

10/18 M no class
10/20 W Bayes Estimators   notes
10/21 F Fall Break

## 10

10/25 M Hypothesis Testing I   notes
10/27 W no class
10/29 F Hypothesis Testing II   notes

## 11

11/01 M Hypothesis Testing III   notes
11/03 W Neyman-Pearson Lemma   notes
11/05 F Neyman-Pearson Lemma   see notes from 11/03

## 12

11/08 M Examples Problem 8.19
11/10 W Examples   notes
11/12 F Problems (end-of-chapter problems from Rice)

## 13

11/15 M Confidence Intervals
11/17 W Confidence Intervals   notes for 11/15 and 11/17
11/19 F Confidence Intervals

## 14

11/22 M ANOVA
11/24 W ANOVA Mathematica notebooks:
Normal, StudentT, FRatio
notes for 11/22 and 11/24
11/26 F Vacation

## 15

11/29 M   Rice, Ch. 9 problems: 13-18, 19-24. Homework: 13, 17, 19 (will discuss Wedn.) notes (answers to take-home)
12/01 W   Mathematica notebook:
Investigating the F distribution
notes (problems 13, 17, 19)
12/03 F     (last class)

12/09 Th FINAL EXAM In regualr room, 10AM--NOON