# Math 5651: Basic theory of probability and statistics

## Fall 2010

 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: Ours is Lecture 001, Tues-Thurs 10:10-12:05am, Vincent Hall 211. (Lecture 002 is taught by Prof. Frank, Tues-Thurs 4:40 P.M. - 6:35 P.M) Office hours: Tues-Thur 9:05-9:55am, and Mon 11:15-12:05am 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 other standard distributions, such as the Bernoulli, binomial, hypergeometric, Poisson, gamma, exponential, beta distributions. Required text: Probability and Statistics, 3rd edition by M. H. DeGroot and M. J. Schervish, Addison-Wesley, 2002. (errata for the text) We hope to do most of Chapters 1-5, and Sections 6.1-6.3, omitting Sections 1.11, 2.4, 2.5, 4.9, 5.8 Another resource: Prof. Charles Geyer's slides and old course notes from when he teachs this class. They're long, but I like them a lot. 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)
18
First midterm 20
Second midterm 20
Third midterm 20
Final exam 20
TOTAL 100
Homework and exam schedule
Homework/exam Due date HW problems/material covered
Math 5651 diagnostic exam
from Prof. Greg Anderson, with a hint for Problem 5:
you can use without proof the fact that
the integral of e-x2 over the whole real line is the square root of Pi.
Tues Sept. 14 Only to be graded for completion;
you must attempt seriously every problem
Chapters 1 and 2 Thur Sept. 23 1.4 # 6(a,d),7
1.5 # 5,9,6,11
1.6 # 4,5
1.7 # 3,4,8,9,10
1.8 # 6,11,15
1.9 # 4,9
1.10 # 2,3,6,11
1.12 # 3,6,7
2.1 # 1,2,5,6
2.2 # 2,7,10,12,17
2.3 # 3,7,8,10
2.6 # 3,14,21,24
First exam Tues Sept. 28
in class
Here is the first midterm with brief solutions, on Chapters 1 and 2.
Chapter 3 Tues Oct. 19 3.1 # 4,5,9,11
3.2 # 5,8
3.3 # 3,4,8
3.4 # 2,4(a,b,c)
3.5 # 3,4,7
3.6 # 8,9
3.7 # 3,4,8
3.8 # 5,7,8
3.9 # 3,7,8
3.10 # 3,5,13
Second exam Thur Oct. 21
in class
Here is the second midterm with brief solutions, covering through Chapter 3.
Chapter 4 Thur Nov. 11 4.1 # 4,5,7,8
4.2 # 3,4,6
4.3 # 3,4,7,9
4.4 # 3,6,7,10
4.5 # 3,6,11
4.6 # 5,6,10,15
4.7 # 2,6,13
4.8 # 1,5,6
4.10 # 5,10,25,27
Third exam Tues Nov. 16
in class
Here is the third midterm with brief solutions, covering through Chapter 4.
Chapter 5 Thur Dec. 9 5.2 # 5,6,9,10
5.3 # 2,3,5,7
5.4 # 3,4,14,15
5.5 # 2,3,6,7
5.6 # 3,4,5,9,10
5.7 # 2,3,8,10
5.9 # 4,6,7,10,13
5.10 # 2,4,7,9
5.13 # 6,13,15
(Sections 5.11, 5.12 were removed)
Chapter 6 Recommended to try,
but not handed in
5.11 # 1,3,5
5.12 # 2,3,4,11
6.2 # 3,4,5,6,11
6.3 # 3,5,6,10,11,14
Final exam Fri Dec. 17 from 8am-10am
in Vincent Hall 211
Here was the final exam with brief solutions, covering the whole course
Back to Reiner's Homepage.