The following calendar reflects topics covered in class and discussions.
On any day, the list of topics is final for all lectures that have already taken place.
The contents of
future lectures and the dates of home assignments are tentative

 
      Week 1
Lecture 1   8/30 Review of probability theory. Probability spaces. BH Sect.1.1

     Discussion 1: Frequently used distributions.

      Week 2
Lecture 2   9/4 Continuity of probability. Independence and conditional probability. BH Sect.1.1,1.2.
Lecture 3   9/6 Borel-Cantelli lemmas. Random variables. Distributions. BH. 1.2, 1.3.
HW1 assigned. solutions
    Discussion 2: Sigma-algebra and Borel algebra.
      Week 3
Lecture 4   9/11 Expectation and other moments. PDFs.

Lecture 5   9/13 Convergence of RVs. Almost sure convergence, conv. in probability. BH.Sect.2.1
     Discussion 3: Infinitely often events, Borel-Cantelli Lemma, expectation.

      Week 4
Lecture 6   9/18 Almost sure and uniform convergence. BH. Sect.2.1
HW2 assigned. solutions
Lecture 7   9/20
Mean-square convergence, convergence in distribution. BH. Sect.2.1
     Discussion 4: Convergence. Especially counterexamples.
 
     Week 5
Lecture 8   9/25 Relations between modes of convergence Laws of large numbers. BH.Sect.2.1,Sect.2.3

Lecture 9   9/27 Definitions for random processes. BH 4.1, ML 2.1
     Discussion 5
A Review first two chapters.
      Week 6
Lecture --  10/2 No class

Lecture 10  10/4 Examples of random processes. Jointly Gaussian RVs. BH 3.4,4.5,4.6; ML2.4
     Discussion 6 Problems in HW2.

HW3 assigned Large size, Due in 2 weeks (on 10/23), solutions

     Week 7
Lecture 11 10/9 Poisson process BH 4.5. Stationarity and Ergodicity BH 4.6; ML 2.2,2.3.

Lecture 12 10/11  Markov processes BH 4.8,4.9; ML2.4. Discrete-time Markov chains.
    
Discussion 7: Properties of Poisson process.
     Week 8
Lecture 13 10/16  Markov processes. BH5.8, 4.9
Lecture 14 10/18 Discrete-time Markov chains. ML3.2
     Discussion 8: Examples of discrete-time Markov chains.

     Week 9
Lecture 15 10/23 Classification of states. ML 3.2.1, 3.2.2. HW4 assigned solutions  

Lecture 16 10/25 Invariant vectors and equilibrium distribution. ML 3.2.3.
      Discussion 9: Examples of discrete-time Markov chains (continued).
     Week 10
Lecture -- 10/30 Sandy, no class

Lecture 17 11/1 Hitting and absorption times. Limiting probabilities. ML Sect.3.2.4, 3.2.3.
      Discussion 10: Problems in HW3.
     Week 11
Lecture 18 11/6 Continuous-time Markov chains (ML Sect. 3.3.1 - 3.3.3)

Lecture 19 11/8 The Poisson process (ML, Sect. 5.1)
     Discussion 11: Examples of continuous-time Markov chains.  
     Week 11
Lecture 20 11/13 The Poisson process, continued (ML. Sect. 5.1)

Midterm 1 11/15 HW5 assigned solutons
     Discussion 12: Discussion of midterm problems (Friday only; no meeting on Thursday)
     Week 12
Lecture 21 11/20  Asymptotics of Poisson Process. Nonhomogeneous Poisson processes. (ML Sect.5.2)
Thanksgiving break 11/21-24
     Week 13
Lecture 22 11/27 Birth-and-Death processes. Explosion (click here). Renewal processes (ML 5.6).
Lecture 2
3 11/29 Conditional expectations. Definition of martingales. Examples. BH 10.1,10.2
      Discussion 13
    Week 14
Lecture 24 12/4 Stopping time of a martingale. Examples. BH 10.4  HW6 assigned solutons

Lecture 25 12/6 Convergence of martingales (click here)
     Discussion 14
    Week 15
Lecture 26 12/11 Concentration inequalitites. BH 10.3; McDiarmid

Final Exam Place: CHE 2108 Date: 12/19, Time 10:30-12:30