Electrical and Computer Engineering

312. Probability and Random Variables.  Basic concepts of probability theory, continuous random variables, distribution, moments and characteristic function, elements of statistics.  Applications to electrical engineering.  Three lectures.  Fall  (Cr.4) 

Prerequisite:  MATH 201.

Goals:           This course is designed to give juniors in Electrical Engineering an

                       understanding of probabilistic and statistical concepts and the ability to

                       select probability models which are useful in solving signal processing,

                       statistical communication and other engineering problems.

Texts:         "Probabilistic Methods in Signal and Systems Analysis", George Cooper,

                      Clare McGillem, 3rd., Ed., 1999, Oxford Press . 

Prerequisite by Topic:

      1.       Derivatives and integrals of functions

      2.       Finite series

      3.       Multiple integrals, Convolution integrals, transformation of variables

Topics:

      1.       Random experiments, definitions of probability, dependent and independent

                events, Bernoulli trials. (8 classes)

      2.       Discrete and continuous random variables, distribution and density functions,

                moments, characteristic function, conditional densities. Examples: Gaussian,

                uniform, exponential, binomial, Poisson and other random variables. (9 classes)

      3.       Two or more random variables, joint statistics, statistical dependence and

                independence, Central Limit Theorem (7 classes)

      4.       Random Processes, statistics of random processes, stationarity, ergodicity

                (6  classes)

      5.       Correlation functions with application to Linear Systems (3 classes)

      6.       Elements of Statistics (6 classes)

      7.       Testing (three tests, final examination) (5 hours)

Computer Usage:

An investigation of random number generation and plotting of well known probability distributions using MATHCAD was assigned.

Statistics Usage:

Statistics is overviewed. Statistical topics investigated in detail include relative and absolute frequency, sampling theory and the sampling mean and variance, and curve fitting with linear regression.  One homework assignment is given which amplifies the last pair of topics. 

ABET category content as estimated by faculty member who prepared this course description:  Mathematics: 3 credits or 100%

Prepared by:   Romeo Pascone