Math 21-325 - Probability theory
Sevak Mkrtchyan
7121 Wean Hall
e-mail: sevakm (at_sign)

Course Description

Concepts covered will include probability spaces, random variables, expectations, conditional probability and independence, limit theorems such as the strong law of large numbers and the central limit theorem, random walks. Additional topics will be covered as time permits.


MWF 9:30-10:20AM in PH 125C

Office Hours:

MWF 8:30-9:20 and 10:30-11:20 (7121 Wean Hall)


The textbook for the course is: Feller, An Introduction to Probability Theory and Its Applications , Volume 1, 3rd edition


Your grade in the class will be based on the following weights:
25% - Homework assignments
20% - Midterm exam 1 (Monday, October 1, in class)
20% - Midterm exam 2 (Monday, November 5, in class)
35% - Final exam


Homework assignments will be posted online and collected in class at the beginning of class on Wednesdays. No late homework will be accepted. The two lowest homework grades will be dropped.

You are allowed to collaborate on homework assignments, however writing up of the solutions should be done individually. You should never share written down solutions which will be submitted as homework by other students.

This is a schedule for what I have covered and what I plan to cover in class each day. This section will be updated regularly during the semester.

Mon, August 27 Introduction. The sample space. Chapter 1.8: 4,16; Sep 5
Wed, August 29 Probabilities. Chapter 2.10: 1,3,4,5,11,15. Sep 5
Fri, August 31 Combinatorial Analysis
Mon, September 3 Labor day; No classes
Wed, September 5 Combinatorial Analysis, Binomial series Chapter 2.10: 17, 19, 27, 32, 38 Sep 12
Fri, September 7 Hypergeometric distribution Chapter 2.11: 3,5,6 Sep 12
Mon, September 10 Waiting times Chapter 2.10: 35,36 Sep 19
Wed, September 12 Random walks Chapter 3.10: 1,2,3,4 Sep 19
Fri, September 14 Random walks - the reflection principle Part of homework 3 Sep 19
Mon, September 17 Random walks - first and last return probabilities Chapter 3.10: 6,7,11,12 Sep 26
Wed, September 19 Random walks - steps on the positive side, maxima
Fri, September 21 Combination of events, Conditional probability Chapter 4.6: 3,8,12,15 Sep 26
Mon, September 24 Stratified populations, Independence Chapter 5.8: 2,6,7,15,16, Oct 5
Wed, September 26 Binomial distribution, law of large numbers Chapter 6.10: 3,5,6 Oct 5
Fri, September 28 Poisson distribution, Poisson process
Mon, October 1 Midterm 1
Wed, October 3 Normal distribution Chapter 6.10: 11,12,17,20,23,27,41 Oct 17
Fri, October 5 Expectation, variance, standard deviation Part of homework 6 Oct 17
Mon, October 8 More on the normal distribution
Wed, October 10 Midterm exam overview
Fri, October 12 DeMoivre-Laplace limit theorem
Mon, October 15 Examples; Normal approximation to the poisson distribution
Wed, October 17 Large deviations Chapter 7.7: 2,4,5,7,9,12,13,14 Oct 26
Fri, October 19 Mid-Semester Break; No Classes
Mon, October 22 Infinite Bernoulli trials
Wed, October 24 Borel-Cantelli Lemmas Part of homework 8 Nov 2
Fri, October 26 Strong law of large numbers Chapter 8: 1,2,3,4,5,6 Nov 2
Mon, October 29 Conditional distribution and conditional expectation Extra credit problem (Blackboard) Nov 9
Wed, October 31 Joint distribution Part of homework 9 Nov 9
Fri, November 2 Covariance Chapter 9: 2,8,9,10,21,34 Nov 9
Mon, November 5 Midterm 2
Wed, November 7 The weak law of large numbers Chapter 10:1,2ab,6,8 Nov 16
Fri, November 9 Absolutely continuous random variables Part of homework 10 Nov 16
Mon, November 12 Joint density, marginals, conditional expectation
Wed, November 14 The partition theorem
Fri, November 16 Transformed random variables Homework 11 Nov 30
Mon, November 19 The multivariate normal distribution
Wed, November 21 Thanksgiving Holiday; No Classes
Fri, November 23 Thanksgiving Holiday; No Classes
Mon, November 26 Generating functions
Wed, November 28 Characteristic functions
Fri, November 30 Proof of the Central Limit Theorem. Brownian Motion Homework 12 Dec 7
Mon, December 3 Brownian Motion
Wed, December 5 Brownian Bridge
Fri, December 7 Construction of a Poisson process

You are expected to attend every class and arrive on time. It is your responsibility to be informed of any announcements made in class.