Math 691-031

Summer I 1998

May 26

**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%

Homework 20%

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

class.

**Course Content and Exam Schedule**

1. Introduction to Probability Theory [Chapter1].

May 26

2. Random Variables [Chapter 2].

May 28

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,

5.1-5.3.3.

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.

June 18

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.

June 30

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.

July 6

14. Renewal reward processes, 7.4.

July 8

15. Final Exam.