Math 481 (Mathematical Theory of Statistics), Section 1, Fall 2026 (Rutgers University)

http://sites.math.rutgers.edu/~zeilberg/math481_26.html

Last Update: Oct. 16, 2026

Textbook

Principles of Statistics , by M.G. Bulmer

[Note: Your classmate Harry asked AI to make a Better looking version , BUT, it is missing some of the homework problems, so to find the homework problems you need to use the original, scanned pdf]

Instructor

Dr. Doron ZEILBERGER ("Dr. Z") [Office: Hill 704; Email: DrZprob at gmail dot com [Note: This Email is ONLY for this class.] ]

Times and Place

TF2 (Tuesdays and Fridays, 10:20-11:40pm) Lucy Stone Hall-B117 (Livingstone Campus)

Dr. Z.'s Office Hours

Hill 704. Tuesdays 2:45-3:30 pm; Fridays: 2:45-4:00 pm.

CLASS POLICY (and grading method)

Lecture Schedule

Mandatory Preliminary Reading: Professor James Norris's Probability Distributions [posted here by kind permison of the author].
Tues. 9/1: Lecture 1 (Chapter 1). Homework: Write a short essay: Is it better to be a Frequentist or a Bayesian?
Added Sept. 1, 2026: today's attendance quiz and here are the Solutions to today's attendance quiz
Fri. 9/4: Lecture 2 (Chapter 2, pp. 12-26). Homework (due 9/18): Excercises 2.1, 2.2, 2.3, 2.4, 2.5. Problems 2.1, 2.6
Added Sept. 4, 2026: today's attendance quiz and here are the Solutions to today's attendance quiz
Tue. 9/8: NO CLASS TODAY (RUTGERS HAS MONDAY SCHEDULE TODAY)
Fri. 9/11, Lecture 3 (Chapter 3, pp. 29-38). Homework (due 9/18): Exercises 3.1,3.3 ; Problems 3.1, 3.2 . Also: Plot the probability function, and cumulative probability function of the random vairable: `Number of goals' defined on the sample space "Players with at least five goals" in the World Cup, using the data given here.
Added Sept. 11, 2026: today's attendance quiz and here are the Solutions (w/o the plots) , Dr. Z's Solutions (with not so nice plots) , and Ashish Manavarthe' Solutions (with nicer plots) ,
Tue. 9/15: Lecture 4 (Chapter 3, pp.38-41). Homework (due 9/25): Exercises 3.4, 3.5; Problem 3.8 [Optional challenge], the best solution will be posted.
Added Sept. 15, 2026: today's attendance quiz and here are the Solutions
Fri. 9/18: Lecture 5 (Chapter 4, pp. 44-59). Homework (due 9/25, modified 9/20, it is OK to use a calculator ):
4.2, 4.3(a), 4.4; Problem 4.1.
Also: using the World Cup Soccer probability function that you did in the extra problem of 9/11: (using the data here), find the mean and variance of the random variable: "Number of goals scored by players who scored at least five goals".
Quiz 1 (on Lectures 1- 3)
Added Sept. 18, 2026: today's attendance quiz and here are the Solutions
Also Added Sept. 18, 2026: today's REAL quiz and here are the Solutions to today's REAL QUIZ
[av=9.42 (out of 10) (sd=1.69)]
Tue. 9/22: Lecture 6 (Chapter 4, pp. 59-65). Homework (due 10/2): [ modified 9/22/26] Excercises 4.10, 4.11; Problems 4.2.
Also: using the World Cup Soccer probability function that you did in the extra problem of 9/11: (using the data here), find the skewness and kurtosis of the random variable: "Number of goals scored by players who scored at least five goals". Is it leptokurtic (i.e. kurtosis larger than 3), or platikurtic (i.e. kurtosis less than 3)?

Added Sept. 22, 2026: today's attendance quiz and here are the Solutions
Fri. 9/25: Lecture 7 (Chapter 5, pp. 68-75). Homework (due 10/2): Excercises 5.1, 5.2, 5.3; Problems 5.1, 5.2 (optional for general h and k; mandatory for the special case k=2, h=1. Hint: write X=A+X1, Y=A+Y1, where A, X1, Y1, are independent and have the same distribution [so the expectations and variances of A,X1,Y1 are all the same]).
Quiz 2 (on Lectures 4 and 5)

Added Sept. 25, 2026: Here is today's attendance quiz and here are the Solutions
Also Added Sept. 25, 2026: Here is today's REAL quiz and here are the Solutions to today's REAL QUIZ
[av=7.46 (out of 10) (sd=3.45)]
Tue. 9/29: Lecture 8 (Chapter 5, pp. 75-77). Homework (due 10/9): Excercises 5.4, 5.6; Also:
Let X be the continuous random variable whose pdf is 2x for x between 0 and 1 and 0 otherwise. (a) Find E[X], the second, third and fourth moments about the origin. (b) Prove that the moment generating function is 2*(exp(t)*t-exp(t)+1)/t^2 (c) Use this to find the first four moments about the origin, and verify that you got the same thing.

Added Sept. 29, 2026: Here is today's attendance quiz and here are the Solutions
Fri. 10/2: Lecture 9 (Chapter 6, pp. 81-90). Homework (due 10/9): Excercises 6.1, 6.2, 6.3. Also:
Quiz 3 (on Lectures 6 and 7)
Added Oct. 2, 2026: Here is today's attendance quiz and here are the Solutions
Also Added Oct. 2, 2026: Here is today's REAL quiz and here are the Solutions to today's REAL QUIZ
[av=7.62 (out of 10) (sd=3.06]
Tue. 10/6: Lecture 10 (Chapter 6, pp. 90-103). Homework (due 10/16): Excercises 6.5, 6.6, 6.7, 6.8, 6.9, 6.10;

Added Oct. 6, 2026: Here is today's attendance quiz and here are the Solutions
Fri. 10/9: Lecture 11: (Chapter 7, pp. 108-115). Homework (due 10/16): Excercises 7.1, 7.2, 7.6; Problem 7.1.
Quiz 4 (on Lectures 8 and 9)

Added Oct. 9, 2026: Here is today's attendance quiz and here are the Solutions
Also Added Oct. 9, 2026: Here is today's REAL quiz and here are the Solutions to today's REAL QUIZ
[av=9.16 (out of 10) (sd=2.15)]
Tue.. 10/13: REVIEW.
Thu. 10/15, 6:30 pm: OPTIONAL SPECIAL REVIEW SESSION (via WebEx, invitations were sent)

recording
Fri. 10/16: EXAM 1 (On lectures 1-11)
Added Oct. 16, 2026: Here is Exam 1 and here are the Solutions of Exam 1.
[av=77.52, s.d.=15.17]
Tue. 10/20: Lecture 12 (Chapter 7, pp. 115-120). Homework (due 10/30): Excercises 7.7, 7.8, 7.9; Problem 7.3.
Fri. 10/23: Lecture 13 (Chapter 8). Homework (due 10/30): Excercises 8.1, 8.2, 8.3; Problems 8.1, 8.5.
Quiz 5 (on Lectures 10 and 11)
Tue. 10/27: Lecture 14 (Chapter 9, pp. 139-154). Homework (due 11/6): Excercises 9.1, 9.2, 9.3, 9.4, 9.5; Problem 9.1.
Fri. 10/30: Lecture 15 (Chapter 9, pp. 154-161). Homework (due 11/6): Excercises 9.6, 9.7, 9.8, 9.9. 9.10, 9.11; Problem 9.3.
Quiz 6 (on Lectures 12 and 13)
Tue. 11/3: Lecture 16 (Chapter 10, pp. 165-176). Homework (due 11/13): Excercises 10.1, 10.2, 10.3, 10.4.
Fri. 11/6: Lecture 17 (Chapter 10, pp. 176-185). Homework (due 11/13): Excercises 10.5, 10.6, 10.7, 10.8; Problem 10.2.
Quiz 7 (on Lectures 14 and 15)
Tue. 11/10: Lecture 18 (Chapter 11). Homework (due 11/20): Problems 11.1, 11.2, 11.3.
Fri. 11/13: Lecture 19 (Chapter 12, pp. 209-221). Homework (due 11/20), Excercises 12.1, 12.2, 12.3; Problem 12.1.
Quiz 8 (on Lectures 16 and 17)
Tue. 11/17: Lecture 20 (Chapter 12, pp. 221-226). Homework (due 12/8), Excercises 12.4, 12.5, 12.6
Fri. 11/20: REVIEW . No quiz today.
Wed. 11/25: EXAM 2 (On lectures 1-19, with some emphasis on lectures 12-19) .
Tue. 12/1: Lecture 21: Perci Diaconis essay on mathematical statistics, chapter VII.10 here (part 1) . Homework: tbd
Quiz 9 (on Lectures 18 and 19)
Fri. 12/4: Lecture 22 : Perci Diaconis essay on mathematical statistics, chapter VII.10 here (part 2). Homework: tbd
Tue. 12/8: Lecture 23: Review
Quiz 10 (on Lectures 20 and 21)
Fri. 12/11: 9:00 am-11:50 am (Optional, but strongly recommended) Marathon review, via WebEx

Final:

Fri. 12/18, 8:00 am-11:00 am in the classrom (Lucy Stone Hall-B117)

Dr. Z.'s teaching