Preliminary lecture (Lecture0)
We covered a quick overview of 2nd year topics including sample spaces, random variables/vectors, pdf's, pf's, functions of rv's and so on ...


Lecture1

summary of the lecture Please read this. It contains some items not given in class.
lecture 1 : Lcture given in class.
suggested work  Includes suggested problems, related text sections, more problems from the text.

some solutions  Here are solutions to some of the suggested problems.

Lecture2
summary of the lecture
lecture2: lecture as given in class.
suggested work

some solutions

Lecture3

summary of the lecture Includes a few new results not presented in class. Please read all of it.

lecture3  The lecture as given in class. Please note the overlap with  some of lecture4 so have a look at the beginning of that document and the sectures of the text related to that ( especially for pgf's and indicator rv's).

suggested work 

Lecture4

lecture: The lecture as given in class with a few pages of  extra important information on elementary conditioning (the conditioning part is mainly a review but make sure you read it and the corresponding sections in the text). There is also a summary of the topics discussed in class.

suggested work: Some readings from the text , suggested problems from the text and some extra problems related to the lecture.

Lecture5

lecture: The lecture as given in class.

suggested work: Read the lecture. Problems and suggested readings from the text. Challenge problem: use the multinomial to derive the joint pdf of the min and max order statistics of a sample of size n from a uniform(0,1) distribution.

Test on Thursday (July 19): 6-9PM
Note: It is extremely important that you write this test ( even if you do not feel totally prepared). The test will cover everything up until Lecture4 and perhaps part of Lecture5.
Lecture6

lecture: Part of the lecture as given in class.

suggested work: Please read the lecture and the suggested sections from the text. There are some important problems that you should do, some of which will be familiar from previous courses.
Lecture7

lecture:  Much of the material here may be found in section 7.5 of the text, but from a characteristic function approach (which we have yet to discuss). In addition, please read Chapter 8 of the text. This chapter was covered in STA257. We also reviewed some of it in the preliminary lecture.

suggested work: p136: 2, 4, 5,11(read); p146: 1, 3, 4, 6, 7, 9; p149 #1.
Lecture8
lecture: characteristic functions, various types of convergence, DCT, CLT, LLN's, probabilistic DCT .

expanded lecture: A few important additions to the one presented in class.

Suggested work: p146 #5; p124 #'s 2(assume convergence for all bounded cts functions), 3 ; p128 #'s 2, 3, 4 ; p130 #'s 1, 2 ; p130 #'s 1, 2 (read them); p135 #'s 1(read), 6 ; p285 #'s 1, 2, 3, 4, 5, 6, 7 ; p287 #'s 1, 2

Relevant sections from the text: 7.1-->7.7, chapter 8, chapter 16   Note: It is important that you read and understand most of the material in these sections, as well as the posted lectures for weeks 8 & 9.

Lecture9
Solution to many problems: Here are solutions to a variety of problems from the text.

Solution to many problems: Here are some important problems along with solutions.

lecture:  The lecture covers renewal processes, basic Markov Chains including simple random walks and branching processes.

Here are a couple of extra problems with solutions.

Lecture10

Review, discussion of the final exam.

The End!!