ECE 60000 - Random Variables and Signals

Course Details

Credits: 3

Areas of Specialization:

  • Communications, Networking, Signal & Image Processing

Counts as:

Normally Offered:

Each Fall, Spring

Requisites by Topic:

Calculus and Fourier transforms

Catalog Description:

Engineering applications of probability theory. Problems on events, independence, random variables, distribution and density functions, expectations, and characteristic functions. Dependence, correlation, and regression; multi-variate Gaussian distribution. Stochastic processes, stationarity, ergodicity, correlation functions, spectral densities, random inputs to linear systems; Gaussian processes.

Required Text(s):

  1. Probability, Random Variables, and Stochastic Processes , 4th Edition , A. Papoulis and S. U. Pillai , McGraw-Hill , 2001 , ISBN No. 9780073660110

Recommended Text(s):

None.

Lecture Outline:

Topic
1 Random experiments
2 Probability spaces
3 Conditional probability
4 Statistical independence of events
5 Compound and repeated random experiments
6 Random variables
7 Probability distributions and density functions of random variables
8 Expectation
9 Characteristic functions and moment generating functions
10 Multiple random variables defined on a random experiment
11 Statistical independence of random variables
12 Correlation
13 Sequences of random variables and stochastic convergence
14 The weak law of large numbers
15 The central limit theorem
16 Stochastic processes
17 Stationarity
18 Correlation and covariance functions
19 Power spectral density
20 Gaussian random processes through linear systems
21 Point and renewal processes
22 The Poisson process
23 Erlang n-th arrival time of a homogeneous Poisson process

Assessment Method:

Exams. (3/2022)