# Math/Stat 431 - Lecture 4: Introduction to the Theory of Probability

Math/Stat 431 is an introduction to the theory of probability, the part of mathematics that studies random phenomena. We model simple random experiments mathematically and learn techniques for studying these models. Topics covered include axioms of probability, random variables, the most important discrete and continuous probability distributions, expectations, moment generating functions, conditional probability and conditional expectations, multivariate distributions, Markov's and Chebyshev's inequalities, laws of large numbers, and the central limit theorem.

Math/Stat 431 is not a course in statistics. Statistics is a discipline mainly concerned with analyzing and representing data. Probability theory forms the mathematical foundation of statistics, but the two disciplines are separate.

Steffen Lempp

### EXTRA TUTORING/OFFICE HOURS:

Conducted by Thomas Hameister in his office B205 Van Vleck at the following hours:
Tuesdays 4:30-6:00 p.m., Thursdays 2:00-5:30 p.m., and Sundays 3:00-4:00 p.m.

### HOMEWORK:

Homework will be due on Wednesdays at the beginning of class.

There will be no credit for late homework except in case of illness or family emergency.

Solutions to some of the problems will be posted on Canvas as soon as I know that I have all the homework (usually by Friday morning).

• HW # 1 DUE 9/13: p. 360, # B.2; p. 373, # C.8, C.16; p. 381, # D.4; p. 34, # 1.2, 1.6, 1.8
(NOTE: C.16 is misstated, please delete "or reflected" from the problem.)
• HW # 2 DUE 9/20: p. 36, # 1.12, 1.16, 1.23, 1.26, 1.32, 1.36, 1.40, 1.44
• HW # 3 DUE 9/27: p. 74, # 2.8, 2.12, 2.14, 2.16, 2.30, 2.36, 2.42, 2.50
• HW # 4 DUE 10/4: p. 76, # 2.22, 2.28, 2.52, 2.64, 2.66, 2.74, 2.78, 2.84
• HW # 5 DUE 10/11: p. 124, # 3.4, 3.6, 3.10, 3.24, 3.30, 3.42, 3.48
• HW # 6 DUE 10/18: p. 125, # 3.14, 3.18, 3.38, 3.46, 3.62, 3.72; p. 165, #4.4, 4.18
• HW # 7 DUE 10/25: p. 165, # 4.8, 4.10, 4.24, 4.26, 4.34, 4.40, 4.44
• HW # 8 DUE 11/1: p. 166, # 4.14, 4.48; p. 188, # 5.2, 5.14, 5.16, 5.18
• HW # 9 DUE 11/8: p. 189, # 5.8, 5.24, 5.30; p. 225, # 6.4 (removed!), 6.6, 6.18, 6.22, 6.24
• HW # 10 DUE 11/15: p. 226, # 6.12, 6.28, 6.36, 6.44; p. 252, # 7.2, 7.20, 7.24
• HW # 11 DUE 11/22: p. 252, # 7.8, 7.28, 7.32; p. 282, # 8.4, 8.22, 8.26
• HW # 12 DUE 11/29: p. 282, # 8.8, 8.10, 8.30, 8.36
• HW # 13 DUE 12/6: p. 283, # 8.16, 8.42, 8.46, 8.52; p. 345, # 10.4, 10.6, 10.20, 10.22
• HW # 14 DUE 12/13: p. 346, # 10.8, 10.26, 10.32 (ignoring the last sentence of the problem), 10.40

### EXAMS:

Makeup exams will be scheduled only with the instructor's consent, and only in case of illness or family emergency.

• Midterm Exam 1: October 18, 7:15-8:15 p.m., B239 Van Vleck, covers material up to and including section 3.4
• Midterm Exam 2: November 15, 7:15-8:15 p.m., B239 Van Vleck, covers material up to and including section 6.3
• Final exam: December 15, 2:45 - 4:45 p.m., 6203 Social Sciences Bldg.

Prepared by Steffen Lempp (@math.wisc.edu">lemppmath.wisc.edu)