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**

**
**

Discussion 1: Frequently used distributions.

Lecture 3 9/6 Borel-Cantelli lemmas. Random variables. Distributions. BH. 1.2, 1.3. HW1 assigned. solutions

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.

Lecture 7 9/20 Mean-square convergence, convergence in distribution. BH. Sect.2.1

Discussion 4: Convergence. Especially counterexamples.

Lecture 9 9/27 Definitions for random processes. BH 4.1, ML 2.1

Discussion 5 A Review first two chapters.

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.

Lecture 14 10/18 Discrete-time Markov chains. ML3.2

Discussion 8: Examples of discrete-time Markov chains.

Lecture 16 10/25 Invariant vectors and equilibrium distribution. ML 3.2.3.

Week 10

Lecture 17 11/1 Hitting and absorption times. Limiting probabilities. ML Sect.3.2.4, 3.2.3.

Lecture 19 11/8 The Poisson process (ML, Sect. 5.1)

Discussion 12: Discussion of midterm problems (Friday only; no meeting on Thursday)

Thanksgiving break 11/21-24

Lecture 22 11/27 Birth-and-Death processes. Explosion (click here). Renewal processes (ML 5.6).

Lecture 23 11/29 Conditional expectations. Definition of martingales. Examples. BH 10.1,10.2

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

Lecture 26 12/11 Concentration inequalitites. BH 10.3; McDiarmid