Probability and Random Processes for Engineers
Fall 2008
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ECE 153 Probability and Random Processes for Engineers Fall 2008 |
| Course Topics |
| Basic Probability: | Probability space and axioms, basic laws, conditional probability
and Bayes rule, independence. [LG 2.1-2.5] Random variables, probability mass function (pmf), cumulative distribution function (cdf), probability density function (pdf), discrete, continuous, and mixed random variables, functions of random variables, generation of random variables. [LG 3.1, 3.2, 3.4-3.6, 4.1, 4.2, 4.4, 4.5, 4.7, 4.9] Pairs of random variables, joint, marginal, and conditional distributions, maximum likelihood (ML) and maximum a posteriori probability (MAP) detection. [LG 5.1-5.5, 5.7, 5.8, 6.5, 8.6] Expectation, mean, variance, characteristic function, covariance and correlation, Markov and Chebychev inequalities, Jensen's inequality, conditional expectation. [LG 4.3, 4.6, 5.7] Minimum mean square error (MMSE) estimation, linear estimation, jointly Gaussian random variables. [LG 5.9, 6.5] |
| Random Vectors: | Extension of cdf, pdf, and pmf to more than two random variables,
independence and conditional independence, covariance matrix,
Gaussian random vectors, linear estimation - vector case.
[LG 6.1-6.5] Modes of convergence, laws of large numbers, central limit theorem. [LG 7.1-7.4] |
| Random Processes: | Discrete-time and
continuous-time random processes, memoryless, independent increment,
Markov, and Gaussian random processes, point processes.
[LG 9.1-9.6] Stationary processes, autocorrelation functions and power spectral density (psd), white noise, bandlimited processes. [LG 9.6, 10.1] Response of linear systems to random inputs, linear estimation - process case, infinite smoothing, Wiener filtering. [LG 10.2, 10.4] |
| Course Outline |
| This is a tentative outline for the course. Changes may be made as the course progresses, and we will update the outline accordingly. Many unlisted side topics will be included when appropriate. |