Summer I 1998
Professor:Dr. S. K. Dhar
Office: Room 327 Cullimore. Phone: X3488
Hours: Tuesday and Thursday 4 pm to 5 pm
(Also by appointment)
Text: Hours: Tuesday and Thursday 1 pm to 4 pm
Introduction to Probability models, sixth
edition, by Sheldon M. Ross.
Text book must be read for the material covered each time in class and make sure that solved problems are understood.
Place & Time: University 202, Hours: Tuesday and Thursday
1 pm to 4 pm
Grade Policy: Mid-term Exam 40%
Final Exam 40%
Homeworks are due within a week from when it is assigned. Late homework can not be accepted. Solution to homework
can be handed in early at the Math main office Cullimore Hall sixth floor, dated and timed by the person receiving it.
Make up: No makeup, except for extenuating
circumstances such as illness, death in the
family, etc., and proof is required (doctors
excuse from class, etc.), the final exam
score will be used to replace the missed
exam. If there is no excuse, you will
receive an "F" for that exam. In the event
that the student will also miss the second
exam due to university-excused absences,
you are encouraged to withdraw from the
Course Content and Exam Schedule
1. Introduction to Probability Theory [Chapter1].
2. Random Variables [Chapter 2].
3. Conditional Probability and conditional expectation June 2 [Chapter 3].
4. Markov Chain 4.1-4.2, Chapman -Kolmogorov
June 4 Equations.
5. Classification of states & limiting probabilities, June 9 4.3-4.4.
6. Some applications of Markov chain, 4.5.
June 11 The exponential distribution, The Poisson Process,
7. Poisson process and its generalizations: Compound
June 16 Poisson and Non homogeneous Poisson Processes, 5.4.
8. Selected Review and Mid-term exam, in class.
9. Continuous time Markov Chains, birth and death
June 23 processes, 6.1 - 6.3.
10. The transition probability function Pij(t), 6.4.
June 25 Limiting Probabilities.
11. Limiting Probabilities, 6.5.
12. Renewal theory and its applications
July 2 Distribution of the counting process N(t), 7.1-7.2.
13. Limit Theorems and their applications, 7.3.
14. Renewal reward processes, 7.4.
15. Final Exam.