MATH
408 Mathematical Statistics
Syllabus [pdf]
Lectures 
MWF
12:0012:50 pm in ZHS
352 
Instructor 

Office 

Email 
kzuev@usc.edu (please
include “408” in the subject line) 
Office
Hours 
MWF
1:302:30 pm, or by appointment 
Discussions 
TTh
9:009:50 am, 10:0010:50 am in KAP
165 
Teaching
Assistant 
Grigory
Sokolov (gsokolov@usc.edu, KAP
415) 
Coure
Description
Mathematical
Statistics is the branch of applied mathematics that studies ways
of drawing inferences from limited data. The main goal of this course
is to give an introduction to the fundamental concepts, ideas, and
methods of Statistics. 
Prerequisites
Textbooks
J.
Rice, Mathematical Statistics and Data analysis, 3rd edition,
2007. 
Course
Plan
The
plan is to cover most of Chapters 611. Topics will include: the
sample mean and the sample variance and their properties; estimation
of population parameters under simple random sampling and stratified
random sampling; confidence intervals; fundamental concepts of statistical
inference; method of moments; method of maximum likelihood; CramerRao
lower bound; sufficient statistics; testing hypothesis; likelihood
ratio test and goodness of fit; probability plots; descriptive methods
for summarizing data; comparing two samples; parametric and nonparametric
methods.

Grading
Homework 
10% 
Quizzes 
10% 
First
Midterm 
20% 
Second
Midterm 
20% 
Final 
40% 

Homework
Homework
problems and due dates will be posted here.
These problems will be collected in Discussion class on Thursday.
Late homework will not be accepted for any reason.

Quizzes
A
quiz will be given every other Tuesday (for exact dates see
“Important Dates” below).
All quizzes are closedbook. Calculators are allowed. 
Midterm
Exams
There
will be two (one hour) midterm exams: Wednesday, February 13
(exam 1) and Wednesday, March 27 (exam 2). The 2nd exam will
cover the material after the 1st exam. Both exams will be given
in regular class time. The place will be announced later. Both
exams are closedbook, but you are allowed to bring one sheet
of formulas. Calculators are allowed. 
Final
Exam
The
final exam will be comprehensive and it will be held at the
time specified in the University
Schedule of Classes: Friday, May 10, 11am1pm, location
to be announced. The final exam is closedbook, but you are
allowed to bring one sheet of formulas. Calculators are allowed. 
Important
Dates
Quizzes 
Jan
22, Feb 5, 19, Mar 5, Apr 2, 16, 30 
Homework 
Jan
25, Feb 8, 22, Mar 8, 29, Apr 12, 26 
First
Midterm 
Wednesday,
February 13 
Second
Midterm 
Wednesday,
March 27 
Final 
Friday,
May 10, 11am1pm 
Expectations
Official
announcements, homework assignments, due dates, solutions
will be posted on the course website. You are expected
to check the course website on a regular basis. You
are encouraged to read the appropriate sections of the
textbook in advance and discuss the homework assignments
with other students. 
Behavior
Behavior
that persistently or grossly interferes with classroom
activities is considered disruptive behavior and may
be subject to disciplinary action. Such behavior inhibits
other students’ ability to learn and an instructor’s
ability to teach. A student responsible for disruptive
behavior may be required to leave class pending discussion
and resolution of the problem and may be reported to
the Office
of Student Judicial Affairs for disciplinary action.
In particular, the use of cell phones during class or
conversation is disruptive behavior. 
Academic Integrity
All
students are responsible for maintaining standards of
academic integrity. The university regards cheating
as a very serious issue and recommends F in the course
for any violation. In particular, collaboration, use
of notes, or any electronic devices during quizzes,
midterms or the final are strictly prohibited. 

Notes
All slides in a single [pdf]
Lecture
1: ABC of Probability [pdf]
Lecture 2: Conditional Probability [pdf]
Lecture 3: Discrete Random Variables [pdf]
Lecture 4: Continuous Random Variables and Transformations of Random
Variables [pdf]
Lecture 5: Joint Distributions [pdf]
Lecture 6: Expectation, Variance, Covariance, and Correlation [pdf]
Lecture 7: Conditional Expectation and Conditional Variance [pdf]
Lecture 8: Inequalities [pdf]
Lecture 910: The Law of Large Numbers & The Central Limit Theorem
[pdf]
Lecture 11: Probability Theory: an Overveiw [pdf]
Lecture 12: Introduction to Survey Sampling [pdf]
Lecture 1314: The Sample Mean and the Sample Variance Under Assumption
of Normality [pdf]
Lecture 15: Accuracy of estimation of the population mean [pdf]
Lecture 16: Estimation of the Population Variance [pdf]
Lecture 17: Normal Approximation to the Sampling Distribution of
the Sample Mean [pdf]
Lecture 18: Estimation of a Ratio and the Delta Method [pdf]
Lecture 19: Stratified Random Sampling [pdf]
Lecture 2021: Neyman Allocation vs Proportional Allocation and
Stratified Sampling vs Simple Sampling [pdf]
Lecture 22: Survey Sampling: an Overview [pdf]
Lecture 23: Fundamental Concepts of Modern Statistical Inference
[pdf]; The Method of Moments
[pdf]
Lecture 2425: The Method of Maximum Likelihhod [pdf]
Lecture 2627: Confidence Intervals from MLEs [pdf];
The Bootstrap Method: Simulation Results [pdf]
Lecture 28: Efficiency and the CramerRao Lower Bound [pdf]
Lecture 2930: Testing Hypotheses: The NeymanPearson Paradigm [pdf]
Lecture 31: Generalized Likelihood Ratio Tests [pdf]
Lecture 3233: Pearson's ChiSquared Test for Multinomial Data [pdf]
Lecture
34: Summarizing Data [pdf]
Lecture 35: Summarizing Data II [pdf]
Lecture 36: Summarizing Data III [pdf]
Lecture 37: Gapminder
Lecture 38: Fundamental Concepts of Statistical Inference [pdf]
Homework
Late
homework will not be accepted for any reason.
(Learn to do things in advance)
# 
Topic 
Problems 
Due
Date 
1 
Conditional
Probability 
Ch.
1, # 7, 45, 65, 75, 77.

Jan 31 
2 
Random
Variables, Joint Distributions, and Expectations 
Ch. 2,
# 31, 59;
Ch. 3, # 15;
Ch. 4, # 21, 49, 67. 
Feb
14 
3 
Limit
Theorems and Distributions Derived from the Normal Distribution 
Ch. 5,
# 13, 15, 19 (for #19, provide a source code you used)
Ch. 6, # 3. 
Feb
28 
4 
Survey
Sampling 
Ch.
7, # 1, 18, 21. 
March
14 
5 
The Method
of Moments & The Method of Maximum Likelihood 
Ch.
8, # 5(a,b,c), 7(a,b). 
April
4 
6 
Testing
Hypotheses 
Ch. 9,
# 1, 7, 9, 17(a,b) 
April
18 
7 
Summarizing
Data 
Ch. 10,
# 1, 11, 16, 19 
May
2 
Solutions
Homework 1 [pdf],
mean=9.55
Homework 2 [pdf], mean=7.53
Homework 3 [pdf], mean=6.11
Homework 4 [pdf], mean=8.45
Homework 5 [pdf], mean=9.10
Homework 6 [pdf]
Quiz
1 [pdf], mean=8.81/10
Quiz 2 [pdf], mean=6.72/10
Quiz 3 [pdf], mean=8.26/10
Quiz 4 [pdf], mean=8.28/10
Quiz 5 [pdf], mean=5.04/10
Quiz 6 [pdf], mean=6.25/10
Midterm
1 [pdf], mean=75.72/100, std=15.95
Midterm 2 [pdf],
mean=78.45/100, std=17.32
More

"The
quiet statisticians have changed our world, not by discovering
new facts or technical developments but by changing the ways
we reason, experiment, and form our opinions,"
Ian Hackling. Well, statisticians are not quiet any more! Watch
The
Joy of Stats, a very inspiring video with Prof. Hans Rosling.
 Hans Rosling
shows
the best stats you have ever seen.
Download the gapminder,
and play with it. It is fun!
 If you
want to quickly refresh your knowledge of Probability and Statistics,
these
notes by Prof. Cosma Shalizi might be useful. These notes are short
and contain the essence.
 If you
like Statistics, I would strongly recommend you to read a nontechnical
book The
Cartoon Guide to Statistics by Larry Gonick and Woollcott Smith.
Here is a brief and subjective review.
 If the
material we cover in class is not enough for you, and you want more,
I would recommend to try All
of Statistics: A Concise Course in Statistical Inference by Larry
Wasserman. It is available online here.
This is a very good book!
