ECEN 3810 ‑ Introduction to
Probability
FALL 2006
Department
of Electrical and Computer Engineering
University of Colorado-Boulder
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Recitation class tomorrow at EE 1B28 from |
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Recitation Class tomorrow at EE265 from |
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Recitation Class tomorrow at EE1B28 from |
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Recitation Class tomorrow at EE1B28 from |
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Recitation Class today at EE1B28 from |
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Recitation Class today at EE1B28 from |
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Recitation Class tomorrow at EE1B28 from |
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Recitation Class today at EE1B28 from |
Instructor: Mahesh Varanasi
Room: ECOT 333 ,
Phone : (303) 492‑0258
Email: varanasi@colorado.edu
Office hours:
5:30-7:30 pm MW, 3:00-4:00 pm F
Teaching Assistant: Rajesh T Krishnamachari
Room : ECEE
150,
Phone: (303)
492-2759
Email: krishnrt@colorado.edu
Office hours:
F 4-5 pm
Course web site:
Lecture Timings: MWF 2-2:50 pm, DUAN G 125
Recitation Class Timings: One of MTF 6-7 pm, EE 1B28
Course Catalog
Description: Covers the fundamentals of
probability theory and treats the random variables and random processes of
greatest importance in electrical engineering. Provides a foundation for study
of communication theory, control theory, reliability theory, optics, and
portfolio analysis.
Course
Objectives: To teach and learn model
building, rigorous probabilistic reasoning and analysis, and probability
calculations in the context of electrical and computer engineering. To solve
problems in gambling, quantizing, communicating, estimating, and quality
control.
Prerequisites: APPM 2350, Calculus 3, and APPM 2360, Linear Algebra and
Differential Equations.
Required ‑ 3 credit hours
Required
Textbook: Probability and Stochastic
Processes (2nd Edition), Yates and Goodman, John Wiley and Sons;
Reference
Textbook: A first course in Probability
(7th Edition) by Sheldon Ross, Prentice-Hall Engineering
Much of our life is
based on the belief that the future is largely unpredictable. For example, we
wouldn’t watch games of chance such as in the U.S. Open or World Cup Soccer or
listen to political pundits talking about the upcoming mid-term elections on TV
if we knew the outcomes in advance. We talk about our belief in this
unpredictability by using words like “random”, “possibility”, “likelihood”,
“risk”, “luck”, ”probability”, etc. and rely on our gaming and other experience
of the world around us to assign qualitative and quantitative meanings to such usages. In this course, we
are interested in constructing a mathematical theory of probability that will
incorporate the concepts of chance which are contained implicitly in common
rational understanding. Such a theory will formalize these concepts as a
collection of axioms, which should lead directly to conclusions that are
consistent with practical experimentation.
Here are some
representative problems from probability theory:
1. Factory 1 makes
twice as many resistors as factory 2 in a week. 20 % of its circuits are
defective (the actual resistance value differs by more than 50 of the stated value) whereas 5 % of those
manufactured by factory 2 are defective. What is the probability that you’d buy
a non-defective resistor?
2. A man is saving up
to buy a new BMW at a cost of N units of money. He starts with k units, 0 <
k < N, and tries to win the remainder by the following gamble with his bank
manager. He tosses a coin repeatedly; if it comes up heads, then the manager
pays him one unit, if it comes up tails, he pays the manager one unit. He plays
this game repeatedly until one of the two events happens that either he runs
out of money or he wins enough to buy the car. What is the probability that he’ll
be ultimately bankrupted?
3. You wish to ask
each of a large number of people to which the answer “yes” is embarrassing. The
following procedure is proposed in order to determine the embarrassed fraction
of the population. As the question is asked, a coin is tossed out of sight of
the questioner. If the answer would have been “no” and the coin shows heads,
then the answer “yes” is given. Otherwise, people respond truthfully.
• a. Can you estimate
the fraction of embarrassed people this way? if so, what is your estimate?
• b. What is the
smallest number of people the examiner must question in order to claim the
probability that his estimate is within 5 % of the true value is not less than
0.95? Assume here that the examiner knows that the true value of the
embarrassed fraction lies somewhere in the interval [0.25, 0.75] ?
4. You roll 6n dice
once; you need at least n sixes. Your friend rolls 6(n+ 1) dice and he needs at
least n + 1 sixes. Who is more likely to obtain the number of sixes he needs?
Grading:
– 25% Homework (Approx. 1 homework per week)
– 10% Pop Quizzes (2-3 during the semester, 20 minutes
each)
– 15% Mid Term I (Oct 4, ’06 from 2-2:50 pm; no class this
day)
– 20% Mid Term II (Nov 8, ’06 from 2-2:50 pm, no class
this day)
– 30% Final Exam (Dec 18, ’06 from 4:30-7:00 pm)
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