Time & Location

Professor

Office hours

Mon, Wed, Fri: 9-10am
1084 East Hall
Kenneth Harris
homepage: kaharris.org
email:
office: 1842 East Hall
tel: 734.763.4703
Mon, Wed, Fri: 10-11, 1-2
(and by appointment)

 

[ Announcements ] [ Course Description ] [ Schedule ]


Announcements

 

Course Description

Prerequisites

Three term calculus sequence. The course will make essential use of the material of Math 116 and 215.

Text

A first course in probability by Sheldon Ross (Seventh edition).

Content

This course introduces students to useful and interesting ideas of the mathematical theory of probability. Topics include the basic results and methods of both discrete and continuous probability theory: conditional probability, independent events, random variables, jointly distributed random variables, expectations, variances, covariances. We will cover most of chapters 1-8 from the textbook.


Grading

There will be 2 midterms (in class), and a final. We will have 11 weekly homework assignments. Grades will be determined by the following weighting.

Homework 25%
Midterm 1 20%
Midterm 2 25%
Final 30%

 

Schedule

Lecture Day Topic Section Notes Homework
1 Jan 7 Basic Principles of Counting 1.1-3 Notes
2 Jan 9 Binomial Coefficients 1.4-5 Notes Homework 1 (due Jan 21)
3 Jan 12 Review of Chapter 1 Notes
4 Jan 14 Probability Models 2.1-2 Notes
5 Jan 16 Axioms of Probabilities 2.3-4 Notes
Jan 19 NO CLASS
6 Jan 21 Sample spaces with equiprobable outcomes 2.5 Notes

Birthday applet
Homework 2 (due Jan 28)
7 Jan 23 Inclusion/Exclusion Principle
Review of Chapter 2
Notes
8 Jan 26 Conditional Probability 3.1-2

Monty Hall Paradox

Notes
9 Jan 28 Bayes Theorem 3.3 Notes Homework 3 (due Feb 4)
10 Jan 30 Independence 3.4 Notes
11 Feb 2 Conditional probability function 3.5 Notes
12 Feb 4 Review of Chapter 3 Notes
13 Feb 6 Discrete Random Variables 4.1-2 Notes

Benford's Law
14 Feb 9 Expectation 4.3-4 Notes

Sic Bo
15 Feb 11 Midterm 1 Chapters 1 - 3 Midterm 1 guide Homework 4 (due Feb 18)
16 Feb 13 Variance 4.4-5 Notes
17 Feb 16 Bernoulli distributions 4.6 Binomial Calculator
Notes
18 Feb 18 Poisson distributions 4.7 Poisson Calculator
Notes
Homework 5 (due March 4)
19 Feb 20 Other distributions 4.8 Notes
Spring Break, No class on week of Feb 23 - 27
20 March 2 Continuous random variables 5.1-2, 5.7 Notes
21 March 4 Uniform distributions 5.3 Notes Homework 6 (due March 11)
22 March 6 Normal distributions 5.4 Notes
23 March 9 Normal distribution 5.4 Notes
24 March 11 Exponential distribution 5.5 Notes Homework 7 (due March 18)
25 March 13 Other continuous distributions 5.6 Notes
26 March 16 Joint distributions 6.1
28 March 18 Independent R.V.s 6.2 Notes
28 March 20 Sums of R.V.s 6.3 Notes
29 March 23 Sums of R.V.s 6.3
30 March 25 Midterm 2 Chapters 4-5 Midterm 2 guide Homework 8 (due April 1)
31 March 27 Conditional distributions 6.4-5 Notes
32 March 30 Joint probability distributions 6.7 Notes
33 April 1 Review Chapter 6 Notes Homework 9 (due April 8)
34 April 3 Expectation 7.1-2 Notes
35 April 6 Expectation 7.2 Notes
36 April 8 Covariance 7.4 Notes Homework 10 (due April 15)
37 April 10 Conditional expectation 7.5-6 Notes
38 April 13 Chebyshev's inequality and the Weak Law 8.1-2 Notes
39 April 15 Central Limit Theorem 8.3 Notes Homework 11 (due April 27)
40 April 17 Strong Law of Large Numbers 8.4 Notes
41 April 20 Chapter 8 Review
April 22 Exam Review
(Not a required class day)
April 27 Final Exam
Monday, April 27
4-6pm