Math 170A: General Course Outline
Catalog Description
    170A. Probability Theory. (4) Lecture, three hours; discussion, one hour. Requisites: courses 32B. Not open to students with credit for Electrical Engineering 131A or Statistics 100A. Probability distributions, random variables and vectors, expectation. P/NP or letter grading.
Textbook
    Sheldon Ross, 7th Ed.
Reviews & Exams
    The following schedule is for 25 lectures. The remaining classroom meetings are for leeway and two midterm exams. For lectures marked with "*" see the comments below.
Schedule of Lectures

Lecture
Section
Topics & Example Numbers
.
.
Combinatorics
1
1.2
Basic principle of counting
2-3
1.3,1.4,1.6
Permutations, combinations, number of ways to distribute distinct and equal objects
.
.
Probabilistic models
4
2.2,2.3
Set theory, axioms of probability
5
2.4,2.6
Properties of probability laws
6*
2.5
Uniform distribution on a ?nite set
.
.
Dependence and independence
7-8
3.2,3.3,3.5
Conditional probabilities and Bayes' formula
9
3.4
Independence of events
10
4.1
Random variables: Basic de?nitions and examples
11
4.9
The cumulative distribution function and its properties
.
.
Discrete random variables
12-13
4.2-4.5
Discrete random variables: probability mass function, ex-pectation and variance
14-15
4.6,4.8.1
Bernoulli, binomial and geometric random variables
16
4.7
Poisson random variables
.
.
Continuous random variables
17-18
5.1,5.7
Continuous random variables: probability density, distribution of a function of a continuous random variable
19
5.2
Expectation and variance of a continuous random variable
20
5.3,5.5
Uniform and exponential random variables
21-22
5.4
Normal random variables, normal approximation
.
.
Jointy Distributed Random Variables
23
6.1
Joint distribution function
24
6.2
Independence of random variables
25*
6.7
Joint distribution of functions of random variables
Comments

To put an emphasis on the problem how to find probabilistic models, lecture 6 can be extended to 2 or 3 lectures, so that the continuous uniform distribution on a bounded set in 1 or 2 dimensions and sequential models also can be covered. A good source for that is Bertsekas/Tsitsiklis (Chapter1.2), see "http://www.athenasc.com/probbook.html".

If time is too short the easiest thing to do is to skip lecture 25.

Outline update: T. Richthammer, 8/08

For more information, please contact Student Services, ugrad@math.ucla.edu.
 

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