MATH 4520/5520

Introduction to Mathematical Statistics

Spring 2021

MWF 04:10 PM - 05:00 PM

Meets Remotely

Instructor: Dr. Janos Englander

Course content:

Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis. Analyzes various distribution-free methods. Prereq: MATH 4510 or APPM 3570, and Calculus 1-2-3. Same as APPM 4520.

How to reach me/office hrs:

  • Office: MATH 324.

  • Zoom Meeting:; Meeting ID: 720 215 9125

  • Office hours: Tuesdays 5-7 on Zoom

  • Phone: 303-492-4846 (with voice mail)

  • EMAIL:

Bad greeting: "Hey Professor"

Okay greeting: "Hi Professor"

Nice greeting: "Dear Professor X"


Grading will be done in two steps:

(1) You can only pass the course if the weighted average of your exams is at least 60, regardless of other factors.

This weighted average is w = (2a+2b+3c)/7, where a and b are the two MT scores and c is the score of the final.

(2) If w=60 or w>60 then we calculate your course grade (different from w), using these weights:

        • Attendance: 10%

        • Homework: 20%

        • Midterm 1: 20 %

        • Midterm 2: 20%

        • Final: 30%

My grader for this semester is Krisztina Dearborn, email:

Please direct questions like "why did I loose 2 points here" to her.

IMPORTANT: HW must be uploaded to Canvas!


First MT: February 22, Monday, in class

Second MT: March 29, Monday, in class

Final: As scheduled by the Office of the Registrar, it will be on TBA

Note: When students have three or more final examinations on the same day, they are entitled to arrange an alternative examination time for the last exam or exams scheduled on that day.

TEXTBOOK: "John E. Freund's Mathematical Statistics with Applications"

(8th Edition)

Important: The textbook should exactly (!) be the hardcover or the paperback shown here: CLICK . It should NOT be the international edition, as it skips certain parts. However, the eTextbook is fine if the same as in this link. For example, the hardcover has these ISBN identifiers: ISBN-13: 978-0321807090 and ISBN-10: 032180709X.

Enrollment questions:

Please see the Registrar's web page, or call their office. If you still have problems, then see Tiffany at the Math. Dept. Office, please.

Help Lab:

The Undergrad Resource Center (a.k.a. Help Lab) is a valuable resource.

Please check the hours of operation at

Material to be covered: We begin with a brief overview of Chapters 1-7 and continue with Chapters 8, 10-14, and some of Chapters 15 and 16, if time permits.

Prereqs and a warning:

MATH 4510 is a prereq, and so is Calc 1-2-3, in particular it is assumed that students are familiar with double and multiple integrals.

How 5520 students are different: Students enrolled into MATH/APPM 5520, will have to do extra homework problems as well as extra problems on the tests.


From Friday to Friday. (With some exceptions.) To find them and to turn in: on Canvas.


If you are a graduate student, then please put a huge "G" at the right top corner of your HW. Thank you. And of course, please try to write in a legible way. Typing would be even better :)

(LaTeX or any other typesetting system is preferred to handwriting. If not, a nice handwriting...)

Numbers will refer to textbook, 8th Edition, with ISBN given above.

Note: The grader will check 3 randomly selected problems, but she will also check if effort was made to solve every problem. The 3 problems will be the same for each UG student.

Some useful links:

Standard Normal Table

Here you have some interesting Statistical Applets and Buffon's Needle Simulation -- take a look.

Example for P-values: click

Explanation on Exponential, Gamma and Poisson: click

Solutions to prior homework: TBA

Chegg policy:

Please do not use Chegg ("ask a question" feature) because:

(1) Chegg's answers are frequently incorrect.

(2) Our department adopted an aggressive policy: posted questions AND answers are requested from Chegg via OIT at CU. Detected cheating results in a 0 score for the whole exam or HW.

Some slides since March 16, 2020 :

4520 Remote teaching, Part 2.pdf
4520 Remote teaching, Part 3.pdf
4520 Remote teaching.pdf


        • Where is the syllabus? A: This web page IS the syllabus.

        • Is the final cumulative? A: Yes.

        • Where are the HW from? A: From the textbook.

        • Where is the funny accent from? A: Hungary.

        • I cannot come to the MT because of health issues or family emergency. What to do? A: Please show me some documentation. I can offer you to skip the MT and calculate your grade based on the other factors, proportionally.

        • Can I turn in the HW late? A: No. Sorry. But remember that the weight of a single assignment is very small.

        • This class is for UG (4520) and Grad (5520) students together. What does this mean in practice? A: HW and exams are slightly extended for grad students. See below.

        • I have an older edition of the textbook. Is it OK? A: Unfortunately, that can be a problem, because the HW might be different.

        • Do we have to remember all those horrible formulas at the exam? A: A cheat sheet will be provided. Tables too.

        • Do I have to write to the instructor because I will skip a class or two? A: No.



IMPORTANT: These two below were mid semester MT's. So only the first questions are relevant for our first midterm! However, we'll have an in-class practice MT.

An old practice MT with solution: CLICK

Solutions to an old Midterm: CLICK

Spring 2020 EXAMS

A practice MT: CLICK

Solutions to MT1: CLICK

A second practice midterm before MT2: CLICK

Solutions to MT2: CLICK

Solutions to MT1

FINAL related STUFF:

Practice Final

Exercises for ML and N-P . (12.12 is the same as Pr 6 in the practice final, except theta_1>theta_0)