Time & Location 
Professor 
Office hours 




[ Announcements ] [ Course Description ] [ Schedule ]
Announcements
 04/28/09: The solutions and statistics for the Final Exam are at statistics and solutions
 04/18/09: Final guide is available. I will have extended office hours on Wednesday (April 22), Friday (April 24) and Monday (April 27) from 10  2.
 03/27/09: Lecture 24 has been corrected (the computation of the gamma function for odd arguments was incorrect).
 03/26/09: Midterm 2 solutions and statistics are posted.
 03/21/09: Homework solutions for Homework 6 and Homework 7 available.
 03/15/09: Midterm 2 guide is available.
 02/04/09: Midterm 1 guide
 02/12/09: Midterm 1 solutions and statistics are posted.
 02/12/09: Midterm 2 is moved back to Wednesday, March 25.
 02/04/09: Midterm 1 guide is available with practice exams..
 01/25/09: Midterm 1 is moved back to Wednesday, February 11.
 01/07/09: Welcome to Math 425: Introduction to Probability.
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 18 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  1.13  Notes  
2  Jan 9  Binomial Coefficients  1.45  Notes  Homework 1 (due Jan 21) 
3  Jan 12  Review of Chapter 1  Notes  
4  Jan 14  Probability Models  2.12  Notes  
5  Jan 16  Axioms of Probabilities  2.34  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  3.12 
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  4.12 
Notes Benford's Law 

14  Feb 9  Expectation  4.34 
Notes Sic Bo 

15  Feb 11  Midterm 1  Chapters 1  3  Midterm 1 guide  Homework 4 (due Feb 18) 
16  Feb 13  Variance  4.45  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  5.12, 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 45  Midterm 2 guide  Homework 8 (due April 1) 
31  March 27  Conditional distributions  6.45  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  7.12  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  7.56  Notes  
38  April 13  Chebyshev's inequality and the Weak Law  8.12  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 46pm 