Units:

12

Description:

Basic probability concepts: Probability space, simple and compound events, statistical independence, and Bayes Rule. Total Probability Concept; Bernoulli trials; Poisson Law. De Moivre-Laplace Theorem. Definition of a Random Variable (RV); Probability distribution of an RV: cumulative distribution function (CDF) and probability density function (PDF). Two Random Variables; several Random Variables. Functions of RVs; conditional distributions; conditional expectations; joint distributions. Moments, generating functions, and characteristic functions of RVs. Chebyshev inequality. Estimation; linear estimation; minimum mean square estimation; and orthogonality principle. Limit theorems; Central Limit Theorem; Law of Large Numbers (both strong LLN and Weak LLN). Definition of a Random Process (RP). Different notions of stationarity. Poisson and Gaussian processes. Autocorrelation and Power Spectral Density (PSD) of an RP. Processing of random (stochastic) processes by linear systems. Ergodicity. Spectral analysis. Matched Filtering. Selected applications from telecommunications, data networking (queuing), Kalman filtering.

Last Modified: 2024-06-28 12:29PM

Current session:

This course is currently being offered.

Semesters offered:

• Fall 2024
• Fall 2023
• Fall 2022
• Fall 2021
• Fall 2020
• Fall 2019
• Spring 2019
• Fall 2018
• Spring 2018
• Fall 2017
• Spring 2017
• Fall 2016
• Fall 2015
• Fall 2014
• Fall 2013
• Fall 2012
• Fall 2011
• Fall 2010
• Fall 2009
• Fall 2008
• Fall 2007
• Fall 2006
• Fall 2005
• Fall 2004
• Fall 2003
• Fall 2002
• Fall 2001
• Fall 2000
• Fall 1999
• Fall 1998