Probability, Spring 2001
Instructor: Prof. Ying-Dar Lin
Email: ydlin@cis.nctu.edu.tw, URL: http://www.cis.nctu.edu.tw/~ydlin
Course Objective:
This course is an introductory course on probability, aiming to motivate students
with applications to computer engineering problems and equip the students with basic
capabilities to model and analyze the real problems that they may encounter in the
future. We first cover basic concepts like discrete/continuous sample space, sampling,
permutation, conditional probability, and sequential experiments. Then, we introduce
some well-known discrete/continuous random variables, and their expected value,
variance, and transform function. Moving from probability of events involving only
one single random variable, we look at the joint behavior of multiple random
variables. Also, sums of independent, identically distributed random variables are
computed. The law of large number and the central limit theorem are hereby
introduced. Some famous discrete/continuous-time random processes (indexed
families of random variables), along with their properties, are reviewed. Finally, the
memory-less Markov processes and their applications to queuing theory for modeling
computer systems are introduced.
Textbook: Alberto Leon-Garcia, Probability and Random Processes for Electrical
Engineering, 2nd edition, Addison Wesley, 1994.
Course homepage: http://speed.cis.nctu.edu.tw/~ydlin/course/cn/prob/index.html
Grade: homework (x6) 24%, midterm 36%, final 40%
Lecture: ED102, 10:10AM-12:00NN Monday, 9:00-9:50AM Wednesday
Course Outline:
1. Probability models in electrical and computer engineering
Probability models, simulation models, examples: packet voice transmission, unreliable
channels, random signals, resource sharing
2. Basic concepts of probability theory
Discrete/continuous sample space, counting methods, conditional probability, Bayes’
rule, independence, sequential experiments
3. Random variables
Discrete/continuous random variables, expected values, variances, transforms
4. Multiple random variables
Pairs of random variables, multiple random variables, correlation, covariance, joint
Gaussian random variables
5. Sums of random variables and long-term averages
Sums of random variables, law of large number, central limit theorem
6. Random processes
Binomial counting process, random walk process, Poisson, etc.
7. Introduction to Markov Chains
8. Introduction to Queueing Theory
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