This course covers the axiomatic foundations of probablility, random variables, functions of random variables, moments and conditional distributions, and sequences of random variables.
Instructor  Dr. M.S. Stone 
Lecture  3:304:45pm TTh, OHE 100 
Office  EEB 500B 
Phone  (323) 7404685 
Messages  (323) 7407875, M. Montenegro 
Office hours  2:003:15pm TTh or make appointments 
TA  Huiwen Li 
Discussion  1:00pm Monday, OHE 100B 
Office  EEB104 
Phone  
huiwen@usc.edu  
Office hours  10am12pm Thursday or make appointments 
Grader  Dan Peng 
Office  EEB 104 
Office hours  
Phone  
dpeng@usc.edu 
Text Books
Required textbook: Probability, Random Variables, & Stochastic Processes(Chap. 19), 3rd edition, A. Papoulis, McGraw Hill, 1991
Recommended textbook: Probability and Random Processes for Electrical Engineering, 2nd edition, A. LeonGarcia, AddisonWesley, 1994

Contents 

Interpretations of probability
Axioms of mathematical probability Probability models 

Conditional probability
Bayes Rule Independent events 

Repeated Trials
Bernoulli Trials Poisson Approximation Gaussian Approximation 

Random Variables (RV's):
Definitions, distribution and density functions Important RV's and their distributions 

Functions of One Random Variable g(X):
Definitions, determination of density functions Mean and Variance Moments Characteristic Functions 

Properties of several RV's:
Joint distribution functions and densities Examples including normal RV's Conditional distributions 

Functions of several RV's:
Transformations Sums of independent RV's 

Moments and conditional distributions
Correlation, covariance Least mean square estimation Orthogonality principle 

Sequences of random variables:
General concepts Law of large numbers Central limit theorem Convergence 












Homeworks are assigned weekly, and are due one week after assigned.
Any violations of the University Student Conduct Code will be referred to the Office of Student Conduct.
Page last updated: Sept. 16, 1998
The contents of this web page may be subject to change. Weekly information will be updated without notice. Change in policies, important dates will be announced in class.