# Math 5651: Basic theory of probability and statistics

## Spring 2018

 Prerequisites: Single and multivariable calculus are a must; either Math 2283 or 3283 or 2574 are recommended. Ability to understand and occasionally write proofs required. Instructor: Victor Reiner (You can call me "Vic") Office: Vincent Hall 256 Telephone (with voice mail): 625-6682 E-mail: reiner@math.umn.edu Classes: I teach two of the three lectures for this course this semester: Lecture 001, Tues and Thurs 10:10-12:05am, Ford Hall B15 Lecture 003, Tues and Thurs 4:40-6:35pm, Tate Hall 120 (Lecture 002 is taught by Prof. Arnab Sen, Tues and Thurs 10:10-12:05am in Ford Hall B80) Office hours: Tues-Thurs 11:35-12:05pm, 6:05-6:35pm, and by appointment. Course content: This is a course in the elements of probability and statistics, including topics such as probability spaces, random variables, their distributions, expected values, variances, law of large numbers, moments, moment generating functions, joint distributions, conditional and marginal distributions, Bayes theorem. We will also discuss the the normal distribution ("bell-shaped curve") and central limit theorem, as well as some of the other standard distributions, such as the Bernoulli, binomial, hypergeometric, Poisson, gamma, exponential, beta distributions. Required text: Probability and Statistics, 4th edition by M. H. DeGroot and M. J. Schervish, Pearson either in the Univ. of Minnesota custom edition that has only Chapters 1-7 or feel free to buy the whole book, although the rest will not be needed. We should do most of Section 1.4-7.3, possibly omitting a few sections (e.g. 1.11, 3.10) Here is a web page of resources, errata for the text. Further resources: Prof. Charles Geyer's slides and old course notes from when he teaches this class; a bit long, but I like them. Another text by Grinstead and Snell Relation to other courses: Math 5651 equals Stat 5101. No credit can be given for Math 5651 if credit has been received for Stat 4101 or Stat 5101. Math 5651 is a reasonable stand-alone course. It also functions as the sole prerequisite for Stat 5102 (mostly statistics), Math 5652 (more probability, stochastic processes), Math 5654 (prediction and filtering). Another reasonable stand-alone course in probability is Math 4653, which is taught at a lower level, and does not function as a prerequisite for the above classes. However one can get credit for Math 5651 after having taken Math 4653. Homework: To be handed in at the beginning of the class period on the due date listed below. Late homework will not be accepted. I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework page with whom they have collaborated.
Diagnostic exam
2
homework
(both quantity and quality)
23
First midterm 25
Second midterm 25
Final exam 25
TOTAL 100
Homework and exam schedule
Homework/exam Due date HW problems/material covered
Diagnostic exam from Prof. Greg Anderson.
Hint for Prob. 5: you can use without proof
the fact that integrating over the real line,
R e-x2 dx = √ π
Tuesday Jan. 23 Only to be graded for completion;
you must attempt seriously every problem
HW 1 Thursday Jan. 25 1.4 # 9
1.5 # 6,8,9
1.6 # 2,4,6,8
1.7 # 6,8,10
1.8 # 4,6,16,19
1.9 # 4,6,8
HW 2 Thursday Feb. 8 1.10 # 2,6,8
1.12 # 6,8,10,11
2.1 # 4,6,11
2.2 # 4,10,16
2.3 # 1,4,8
2.4 # 2
2.5 # 6,12,24
First exam Thursday Feb. 22 in class Exam 1 covered Chapters 1, 2, and Sec. 3.1.
Median and average scores approx. 90/100
Lec 001 Exam and answer key
Lec 003 Exam (Lec 003 answer key got corrupted, sorry
-- but it's similar to the one for Lec 001)
HW 3 Thursday Mar. 1 3.1 # 10
3.2 # 6,10
3.3 # 4,8,12
3.4 # 2,8,10
3.5 # 2,6,10
3.6 # 2,8,12
HW 4 Thursday Mar. 22 3.7 # 2,6,8
3.8 # 4,14
3.9 # 4,8,16
3.11 # 6,8,14,22
4.1 # 4,6,8
Second exam Thursday Mar. 29 in class Exam 2 covered Sections 1.4-4.2,
with greatest emphasis on 3.1-4.2
Median score approx. 87/100, average score approx. 84/100
Lec 001 Exam and answer key,
Lec 003 Exam and answer key.
HW 5 Thursday Apr. 12 4.2 # 4, 10
4.3 # 4, 6
4.4 # 6, 8, 10
4.5 # 4, 6, 12
4.6 # 2, 5, 10, 18
4.7 # 2, 6, 8
4.9 # 10, 16
HW 6 Thursday Apr. 26 5.2# 6,10
5.3# 2,6
5.4# 6,8
5.5# 5,6
5.6# 6,14
5.7# 1,8
5.8# 4
5.11# 2,12,16
(removed Sec. 5.10 problems)
Chap. 6,7 problems to try
(not to be handed in) 5.10# 2,8
6.2# 2,6,7
6.3# 4,8
7.3# 5,14
Final exam
Lec 001 Tue May 8
at 10:10am-12:10pm in Tate Hall B65

Lec 003 Tue May 8
at 4:40-6:40pm in Tate Hall 120
Covered whole course, but emphasis on
material since Exam 2; none of Section 5.10.
Median 87/100, average 82/100
Final exam and Final answer key
Back to Reiner's Homepage.