The following calendar reflects topics covered in
class and discussions. HW3 assigned Large size, Due in 2 weeks (on 10/23), solutions
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.