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EE
313
Title:
PROBABILITY FOR ELECTRICAL ENGINEERS
Credits: 4
Catalog Description:
Probability for Electrical Engineers (4+1+0) 4
Fundamentals of probability. Random variables, distribution and density
functions and some
specific functions. Operations on one random variable: expectation,
moments and transforms
of random variables. Vector random variables, joint distribution and
density functions.
Statistical independence. Operations on multiple random variables. Some
basic probabilistic
processes. Random processes, stationarity, independence and ergodicity,
correlation function.
Spectral characteristics of random processes. Linear systems with random
inputs.
Coordinator:
Aysın Ertüzün, Professor of Electrical Engineering
Goals:
The course is designed to familiarize students with the modeling and
analysis of
random phenomena. Basic notions of probability theory as well as methods
of modeling
basic probabilistic and stochastic phenomena are introduced. Students
will couple
engineering intuition with mathematical principles and develop insight
into how to apply
probability theory to practical situations.
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, output of linear systems driven by random
processes
bot in time and frequency domains
Textbook:
R.D. Yates and D. J. Goodman, Probability and Stochastic Processes- A
Friendly
Introduction for Electrical and Computer Engineers, John Wiley & Sons,
Inc., 2005 (2/e)
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. Discrete, continous and mixed random variables, probability mass
funcitons,
probability distribution functions, probability density functions,
cumulative
distribution functions, mean and variance (2 weeks)
4. Families of continuous and discrete random variables
5. Pairs of random variables and joint probability functions
6. Random vectors and probability functions associated with them
7. Applications of s and z transforms to probability distribution
functions and probability
density functions, sums of random variables (2 weeks)
8. Gaussian probability density and the Central Limit Theorem (1.5
weeks)
9. Stochastic processes, independent identically distributed random
sequences, Poisson
processes,Expected value and correlation, stationarity and wide sense
stationary
processes, ergodicity, Cross correlation, Gaussian processes
10. Linear filtering of a continuous-time stochastic process and a
random sequence, Power
spectral density of a continuous-time stochastic process and a random
sequence,
Cross spectral density, Frequency domain filter relationships
11. Markov Chains- if time permits
Course Structure: The class meets for four lectures (two 50-minute
sessions) and a problem
sessions a week( a 50-minute session). Example problems are solved the
problem sessions
held by the teaching assistant. There are two closed-book in-class
mid-term exams and a
closed-book final exam. A formula sheet is given by the instructor.
Computer Resources:
None.
Laboratory Resources:
None.
Grading:
1. Two mid-term exams (30% each)
2. A final exam (40%)
Outcome Coverage:
(a) 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.
(e) 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:
Aysın Ertüzün
Last revised:
March 8, 2009.
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