Probability and Statistics

EECE-340: Probability and Statistics

Term: Fall 2003

Instructor: Balu Santhanam

Pre-requisites: EECE-314, Math-314. Basic knowledge of MATLAB helpful.

Course Abstract: Probability axioms, random variables, mean, variance, Chebyshev inequality, characterisitic functions, transformations of random variables, confidence intervals, jointly defined random variables, multivariate Gaussian variables, conditional probability densities, random processes, correlation, power spectrum, white noise, transmission of noise through LTI systems.

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Announcements :

Note that Midterm II and the review session have been postponed Midterm II, Mon, Nov. 23, 1:00 - 1:50 Midterm Exam II will cover material from PS # 3.0-- 5.0 Review Session for Midterm II will be in Room 118, Thurs, Nov. 22, 2-4 PM (after class)

Course Materials:

Course Outline/Syllabus

EECE-314 review material:

Notes on convolution notes on Fourier Series

Class Notes :

Section I :

Definition of Probability Counting Rules On Classification of Events Notes on Bayes Theorem Notes on the Binomial probability law Notes on the Geometric probability law

Section II : Random Variable

Definition of a Random Variable On the toss of a coin Discrete Random Variable On Characteristic Functions On Expected Values Example 1.0 with Characteristic functions Example 2.0 with Characteristic functions Notes on the Gaussian Integral Notes on Transformation of Random Variables Examples on Transformation of Random Variables Notes on Uniform Quantization Uniform Quantization Example

Section III : Random Vectors

Notes on Second-order Statistics Independence and Uncorrelatedness Notes on the Multivariate Gaussian Plot of the 2D Gaussian and Equiprobable Contours Notes on Transformation of Random Vectors Notes on Order Statistics Covariance Matrices White Random Vectors Notes on Fading

HOMEWORK ASSIGNMENTS:

Problem Set # 1.0 Problem Set # 2.0 Problem Set # 3.0 Problem Set # 4.0 MATLAB Project Guidelines for MATLAB Project Problem Set # 5.0 Problem Set # 6.0 Electronic reserves

Quizzes and Exams :

Quizzes and Solutions Midterm Exam I Make-up Midterm I Midterm Exam II Final Exam

MATLAB FILES:

MATLAB program for dice throw simulation Uniform Quantization Function Random Number Generator for Specified CDF's. Multivariate Gassian Random Vector Function Rayleigh and Rician Envelope Fading Function Sample Output from fade.m: (a) Rayleigh Envelope, (b) Rician Envelope