EE 313

Title: PROBABILITY FOR ELECTRICAL ENGINEERS

Credits: 4

Catalog Description: Fundamentals of probability: Definition of sample space, axiomatic and relative frequency definitions of probability; compound and conditional probability, independence of events, Bayes’ Theorem, combinatorics. Random variables: probability mass functions, probability distribution functions, expected value and variance. Transforms and their application to sums of independent random variables. Some basic probabilistic processes: Bernoulli, Poisson, renewal processes and random incidence. Disrete-state Markov processes, ergodicity and calculation of the limiting state probabilities. Fundamental limit theorems: Laws of Large Numbers, Gaussian distribution and its properties, Central Limit Theorem. Introduction to statistics: Definition of statistic, testing methods, estimation, Bayesian analysis.

Coordinator: Yağmur Denizhan, Associate Professor of Electrical Engineering

Goals: This course aims to expose the students to modelling and analysis of random phenomena.  Basic notions of probability and statistics as well as methods of modelling basic probabilistic and stochastic phenomena are introduced. 

Learning Objectives:

At the end of this course, students will be able to:

1. Model simple probabilistic and stochastic phenomena mathematically.
2. Calculate probabilities of events in a known event space, expected values and variances of random variables, and limiting state probabilities of ergodic processes.

Textbook: Alvin V. Drake, Fundamentals of Applied Probability Theory, McGraw-Hill Inc., 1967.

Reference Texts:A. Papoulis, Probability, Random Variables, and Stochastic Processes, Mc Graw Hill, 1984.

Prerequisites by Topic:

1. Linear algebra
2. Laplace Transform

Topics:

1. Historical background of probability
2. Set theory, events, sample space, definition and axioms of probability (1 week)
3. Random variables, probability distribution functions, probability density functions, cumulative distribution functions, mean and variance (2 weeks)
4. Applications of s and z transforms to probability distribution functions and probability density functions, sums of random variables (2 weeks)
5. Basic probabilistic processes: Bernoulli and Poisson processes (2 weeks)
6. Discrete-state Markov processes, ergodicity and limiting state probabilities (2 weeks)
7. Laws of Large Numbers, Gaussian probability density and the Central Limit Theorem (1.5 weeks)
8. Introduction to statistics (1 week)
9. Significance and hypothesis testing (1 week)
10. Estimation (0.5 week)
11. (Time permitting) Bayesian analysis

Course Structure: The class meets for four lectures and two problem sessions a week, each consisting of two 50-minute sessions. Example problems are solved and quizzes are given during the problem sessions held by the teaching assistant. 6-7 quizzes are given per semester.  There are two in-class mid-term exams and a final exam.

Computer Resources: None.

Laboratory Resources: None.

Grading:

1. Quizzes (20%)
2. Two mid-term exams (25% each)
3. A final exam (30%)

Outcome Coverage:

• Apply math, science and engineering knowledge. Different tools from mathematics (Boolean algebra, linear algebra, Laplace and z-transforms) are heavily drawn upon during lectures, homework sets and exams.

• Identify, formulate, and solve engineering problems. This course is about formulating mathematical models for life-like probabilistic phenomena and solving for some statistics of interest. 30% of the semester is dedicated to applying the theoretical knowledge to typical daily-life and engineering problems.

Prepared By: Yağmur Denizhan

Last revised: May 14, 2003