# ECE 528:Introduction to Random Processes in ECE

**Syllabus PDf:**ECE 528 Syllabus

Course Number | ECE 528 | |

Prerequisites | Prerequisites: ECE 220 and STAT 346 (all with grade of C or better), or permission of instructor. | |

Instructor: | Bijan Jabbari, Professor | |

Semester: | Fall 2020 | |

Lecture Time: | Wednesday 7:20-10:00 pm | |

Location: | Online | |

Office: | Eng. Bldg. Room 3232 | |

Office Phone: | 703-993-1618 (use email only) | |

Email: | bjabbari@gmu.edu | |

Web: | http://cnl.gmu.edu/ | |

Office Hours: | by appointment | |

Teaching Assistant: | Haotian Zhai (email: hzhai@gmu.edu) | |

Office Hours: | Monday and Wednesdays: 9:30-10:30 am | |

Administrative Assistant: |
N/A | |

Course Description |
Probability and random processes are fundamental to communications, control, signal processing, and computer networks. Provides basic theory and important applications. Topics include probability concepts and axioms; stationarity and ergodicity; random variables and their functions; vectors; expectation and variance; conditional expectation; moment-generating and characteristic functions; random processes such as white noise and Gaussian; autocorrelation and power spectral density; linear filtering of random processes, and basic ideas of estimation and detection. |

# Course Outline

- Probability Models in ECE
- Review of probability: set theory, basic concepts, probability spaces, conditional probability, Bayes’ Rule, independence, Borel Fields, Generation of random numbers
- Discrete Random Variables: Notion of Random Variables, Probability Mass Functions (PMF), Expected Value and Moments, Important Discrete Random Variables, Generation of Discrete Random Variables
- General Random Variables (Single Variable): Cumulative Distribution Functions (CDF), Probability Density Functions (PDF), functions of random variables, expectations and characteristic function, Markov and ChebyShev inequalities
- Pairs of Random Variables: joint and marginal distributions, conditional distributions and independence, functions of two random variables, Expectations and correlations, pairs of jointly Gaussian Random Variables, generating jointly Gaussian Random Variables
- Random vectors: Functions of several random variables expected value of vector random variables, jointly Gaussian Random vectors, convergence of random sequences
- Sums of random variables and long-term averages: the sample mean and the Laws of Large Numbers, the Central Limit Theorem
- Stochastic Processes: Basic concepts, Covariance, correlation, and stationarity, Gaussian processes and Brownian motion, Poisson and related processes, Power spectral density, Stochastic processes and linear systems
- Markov Processes and Markov Chains

# Textbooks and References:

- Probability, Statistics, and Random Processes, 3rd Edition, by Alberto Leon-Garcia, Pearson Prentice Hall, 2008.
- D. P. Bertsekas and J. N. Tsitsiklis, Introduction to Probability. Athena Scientific, Belmont, MA, 2nd Edition, 2008. See http://www.athenasc.com/probbook.html

# Grading:

There will be weekly assignments, one Mid-term exam, and a Final exam. They will count towards the grade as follows:

- Homework and MATLAB Projects 20%
- Mid-term 35% (in October)
- Final Exam 45% (up to 2 hours and 30 minutes)