This is an introduction course to random analysis at graduate level which helps to build the theoretical foundation for students in communication, signal processing and networking areas. Topics include probability and random variables; random processes and sequences; linear system response to random input; special classes of random processes. Applications to signal detection and estimation are discussed throughout the course.
Linear system theory and random signal theory at undergraduate level.
Dr. Osvaldo Simeone
Email: osvaldo.simeone@ njit.edu
Phone: (973) 5965809
Office: 101 FMH Building
Office Hour: Wednesday 46pm
Intuitive probability and random process using MATLAB
Steven Kay
Springer, 2006. (a partial electronic version can be downloaded here)
There will two short tests (30% of grade), one midterm (30%), and one final exam (40%). Some of the problem sets will involve Matlab simulation. You can obtain a copy of Matlab software from the campus computing facility (here is a Matlab primer).
Weekly problem will be assigned and due the following class. The assignments will not be graded, but meant as an essential tool for the student to learn and for the teacher to assess the level of preparation of the class. (Cheating on assignments is then doubly inadvisable: it does not help the learning process and gives the teacher the wrong impression that the class is well prepared)
Spring 2006
Final grades (A: 910; B+: 8.59; B: 7.58.5; C+: 77.5;
C: 67)
Final v. A and final v. B
Fall 2007
Announcements:
 Sept. 27^{th}
class has been moved to Monday Sept. 25^{th} in the same classroom (FMH
408) at the usual time (69pm).
 The first
test will be on Oct. 4: one hour (67pm), open books and notes.
 The
midterm will be on Oct. 25: three hours (69pm), one formula sheet allowed.
Links:
 a web page on
the Monty Hall problem.
 a compendium
on common probability mass functions and probability distribution functions
Suggested “light” reading

a
book on how everything
is connected (and the role of probabilistic models in investigating the
problem)

a
book on how order
emerges from chaos (and the role of probabilistic models in investigating
the problem)
Tests:

first test (Oct. 4) – solution
and grades.

midterm (Oct. 25) – solution
and grades.

second test (Nov. 29)  solution
and grades.

final (Dec. 20)  solution
and final grades.
Week 
Date 
Plan 
Chapter covered^{*}^{} 
Homework 

1 
Sept. 6 
Probability, conditional probability (1) 

(+
1 extra problem) 

2 
Sept. 13 
Probability, conditional probability (2) 


3 
Sept. 20 
Discrete random variables 


4 
Sept. 25 
Continuous
random variables 


5 
Oct. 4 
Discrete
multiple random variables 


6 
Oct. 11 
Continuous
multiple random variables 


7 
Oct. 18 
Limit
theorems 



8 
Oct. 25 
Midterm 



9 
Nov. 1 
Random processes, stationarity
(1) 
Ch. 16, 17 

10 
Nov. 8 
Random
processes, stationarity (2) 


11 
Nov. 15 
Linear
systems and stationary processes (1) 


12 
Nov. 29 
Linear
systems and stationary processes (2) 



13 
Dec. 6 
Gaussian
and Poisson processes 



14 
Dec. 13 
Markov
chains 



15 
Dec. 20 
Final 


*See class notes for sections
covered.