4 units – Fall, Spring Quarters

**Lecture:** 3 hours

**Discussion:** 1 hour

**Prerequisite:** EEC 100, ENG 6 or MAT AL

**Grading:** Letter.

**Catalog Description:**

Probabilistic and statistical analysis of electrical and computer systems. Discrete and continuous random variables, expectation and moments. Transformation of random variables. Joint and conditional densities. Limit theorems and statistics. Noise models, system reliability and testing.

**Expanded Course Description:**

- Sample space and probability
- Events, axioms of probability
- Conditional probability, Bayes law
- Independence

- Discrete random variables
- Probability mass function
- Expectation, mean, variance
- Generating function
- Joint probability mass function of multiple discrete random variables
- Conditioning, independence

- Continuous random variables
- Cumulative probability distribution function and probability density
- Expectation, mean, characteristic function
- Transformation of a random variable

- Joint random variables
- Joint probability distribution and densities
- Joint moments
- Transformation of multiple random variables
- Conditional densities, conditional expectation, repeated expectations

- Sums of random variables
- Convergence of sequences of random variables
- Law of large numbers
- Central limit theorem
- Sampling statistics: sample mean, sample variance, confidence intervals

- Random processes
- Sample paths
- Mean, autocorrelation, autocovariance
- Random processes through linear filters
- Autocorrelation of modulated signals (optional)
- Thermal noise in electrical circuits (optional)
- Power spectral density

- Discrete-time Markov chains
- State transition diagram, one step transition matrix of a finite state homogenous Markov chain
- Computation of probability distribution,
*k*step transition probability matrix - State classification
- Steady-state behavior
- Application of Markov chain models to computer systems performance analysis

- Queueing Systems
- Poisson process
- Basic queueing theory:single server system
- Statistical analysis of queueing

**Computer usage:**

MATLAB will be used to simulate random variables and systems, to evaluate signal statisitics, for signal detections and system identification.

**Textbook/reading: **

- C. Therrien and M. Tummala, Probability for Electrical and Computer Engineers, CRC Press.
- D. Bertsekas and J. Tsitsiklis, Introduction to Probability, Athena Scientific.
- R. Yates and D. Goodman, Probability and Stochastic Processes – A Friendly Introduction for Electrical and Computer Engineers, J Wiley & Sons.

**Relationship to Outcomes:**

Students who have successfully completed this course should have achieved:

Course Outcomes | ABET Outcomes |

An ability to apply knowledge of mathematics, science, and engineering | A |

An ability to design and conduct experiments, as well as to analyze and interpret data | B |

An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice. | K |

**Course overlap:**

The first part of the course overlaps with ECI 114, Stat 120 and Math135A, but examples will focus on electrical and computer engineering applications. The material on filtering of random processes, autocorrelations of signals, noise analysis, the power spectral density, Markov chain models of computer systems, and queuing analysis does not overlap with existing courses.

**Professional Component:**

Engineering Depth

Engineering Science: 2 credits

Engineering Design: 2 credits