S. Ross, Introduction to Probability Models, Eleventh Edition.
Additional References:
S. Karlin and H. Taylor, A First Course in Stochastic
Processes, contains a more theoretical
treatment of many of the topics of this course.
P. Hoel, S. Port, and C. Stone, Introduction to Stochastic
Processes, is a classical introduction to stochastic processes.
H. Taylor and S. Karlin, An Introduction to Stochastic
Modeling, is similar in breadth and depth as our textbook.
Prerequisites: Introductory probability (Math 244 or Math 333),
linear algebra (Math 337), and
familiarity with basic ordinary differential equations.
Examinations: There will be a midterm examination
and a final examination.
The midterm examination will occur before the "drop'' deadline. The final
examination date, time, and location will be determined by the university.
Homework: Homework assignments/projects will be given frequently.
Each assignment must be turned in at the beginning of class. Late
assignments are NOT accepted. Early assignments are always welcomed
and are appropriate for preplanned absences from class.
Your work must be shown in order to receive credit.
As a standing assignment,
you should read the relevant sections of the textbook prior to lecture.
Quizzes: From time to time, quizzes may be given. Make up
quizzes are NOT given.
Grading: The midterm examination will represent 35% of your grade.
The final examination will also be worth 35% of your grade. The remaining
30% of your grade will be determined by your homework and
quizzes; in calculating this quantity,
I will drop your one lowest homework or quiz score
from throughout the semester.
Attendance: Attendance at and participation in all lectures
is expected. If you know in advance that you will be absent from class for
a legitimate reason, please tell me prior to your absence so that appropriate
arrangements (if any) can be made. Tardiness to class is very disruptive
of the classroom environment and should be avoided.
Academic Integrity Code: The
NJIT Academic Integrity Code applies
to all activities associated with the course, including but not limited to
homework, quizzes, examinations, and projects. As an example, when you submit
a homework assignment, you are certifying that your paper contains only
your work and is not copied from other people or sources.
Course Topics:
Review of basic probability, common discrete and continuous
distributions, moment generating functions, conditional probability
Discrete-time Markov chains,
Chapman--Kolmogorov equations, classification
of states, limiting probabilities,
mean time in transient states, applications
Exponential distribution, Poisson processes
Continuous-time Markov chains, birth and death processes,
transition probabilities, time reversibility