Math 170B: General Course Outline
Catalog Description
    170B. Probability Theory. (4) Lecture, three hours; discussion, one hour. Requisite: course 170A. Convergence in distribution, normal approximation, laws of large numbers, Poisson processes, random walks. P/NP or letter grading.
Textbook

    Introduction to Probability by D. P. Bertsekas and John N. Tsitsiklis, 2nd edition

    Comments:

    (a) The theoretical problems, which appear with full solutions at the ends of the chapters, are an essential part of the course. Many of them should be incorporated into the lectures. Some to emphasize are given in parentheses below.

    (b) Unfortunately, solutions to all of the other problems are freely available on the book’s web site. Additional problems (with no posted solutions) are available at http://www.athenasc.com/prob-supp.html
Schedule of Lectures

Lecture
Section
Topics and Example Numbers
   
Further Topics on Random Variables
1-3 4.1 Derived Distributions
4-5 4.2 Correlation (see comment below)
6-7 4.3 Conditional Expectation and Variance (problem 28)
8-9 4.4 Transforms
10 4.5 Sum of a Random Number of Independent RVs.
11   Midterm Exam
     
    Limit Theorems
12 5.1 Markov and Chebyshev Inequalities
13 5.2 Weak Law of Large Numbers
14 5.3 Convergence in Probability
15-16 5.4 Central Limit Theorem
17-18 5.5 Strong Law of Large Numbers
     
    Bernoulli and Poisson Processes
19-21   19-21 6.1 Bernoulli Process
22   22 Midterm Exam
23-26   23-26 6.2 Poisson Process
27-28   27-28 Random Walks or Estimation (see comment below)
     
    Additional comment: A good source of supplementary material is Feller, Volume 1. Section 4.2 of the text is a bit weak, and can be supplemented with Chapter IX of Feller. Lectures 27-28 on random walks can be based on Chapter XIV of Feller. An alternative is to spend the last two lectures on applications to estimation, based on Section 9.1 of the text.

Outline T. Liggett 4/10
For more information, please contact Student Services, ugrad@math.ucla.edu.
 

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