Description:
Introduction to fundamental ideas and techniques of stochastic
modeling, with an emphasis on the applications. After reviewing the
basic concepts of probability theory, the course will move quickly
towards the development of probability models and their use in
engineering and sciences. Assignments will very likely involve some
programming.
Prerequisite: An introductory
course in probability theory and some basic linear algebra.
Syllabus:
Rapid review of basic concepts of probability theory (3 lectures):
 Continuous and discrete probability
distributions. Conditional probability and independence. Examples
of probability distributions.
 Random variables: expectation,
standard deviation. Independence and conditional probabilities of
random variables. Joint distributions of random variables:
conditional distributions and expectations, covariance and
correlation.
Introduction to stochastic processes and
Markov chains.
Stochastic models are widely applicable to
the study of many "realworld" phenomena. The course will
develop applications in selected areas such as:
 Information Theory.
 Signal processing.
 Genetics.
 Queuing, waiting line theory. Analysis of
stochastic queuing models.
 Simulations and scientific computing.
 Finance.
Textbooks:
 Sheldon Ross "Introduction to Probability Models"
Academic Press. (required)
 Howard Taylor and Samuel Karlin "An Introduction to
Stochastic Modeling" 3rd. Edition, Academic Press. (optional)
 Howard Taylor and Samuel Karlin "A first Course in
Stochastic Processes" 2nd. Edition, Academic Press.
(optional)
 William Feller "An Introduction to Probability Theory and its Applications" Wiley. (optional)
Handouts:
I will do my best to
post online all the handouts given in class. By the way,
Sheila Shull (217 Firestone) is a person you can contact
at any time (between 9:30am and 5pm) if you need
administrative information. Her phone number is
6263954560.
Teaching
Assistant and Office Hours:
Hannes Helgason, hannes@acm.caltech.edu
Monday 23 p.m., Guggenheim
226.
Lei Zhang, zhanglei@acm.caltech.edu
Tuesday 910:30 a.m., Firestone 214.
Grading:
Homework assignments: 60%
Homework will generally be distributed on Wednesdays and
due in class the following Wednesday.
There will be about 5 or 6 assignments, and your
lowest score will be dropped in the final grade.
Late homeworks will NOT be accepted for grading
(medical emergencies excepted with proof).
Final exam: 40%. There will be a
takehome final exam.
