MATH 571, Introduction to Probability Models

Homework Assignments

Chapter 3:

2, 3, 12, 15, 16, 18(G), 21(G), 36, 37, 47(G), 48(G).

Chapter 4:

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 16, 17, 19, 20, 23, 24, 29, 30, 31, 35, 45, 58(G), 64, 66.

Chapter 5:

1, 3, 14(b), 35, 36, 37, 39, 42, 57.

Chapter 6:

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 22(G), 23(G).

Chapter 10:

1, 2, 4(G), 9, 10, 12, 14, 15, 16, 17, 18(G), 19(G), 25, 26, 27, 30.

Course Information

Meeting Times: 2:00-3:15 pm, MW

Room: PHY 144

Office Hours: 3:20-4:20 pm, MW.

Textbook: S.H. Ross, Introduction to Probability Models, 9th Ed., 2007.

Attendance: Attending lectures regularly is in your own interest. Attendance will be occasionally monitored.

Course Description: This course is a natural extension to any first course in probability or statistics for students interested in modeling physical phenomena by probabilistic rather than deterministic methods. We will study Markov chains in general in both continuous and discrete time. Particular models include queues, branching processes, birth and death models, Poisson processes, and Brownian motion. The focus is on applications rather than theory. For example, we will derive the Black-Scholes pricing formula for stock options and use it to price simple European calls.

Prerequisites: As you might expect, the course supposes familiarity with basic ideas in probability. These are summarized in the first three chapters of the textbook. Students are expected to be fluent with this material. In addition, we will suppose that you have fundamental computational skills in matrix algebra, including the computation of eigenvectors and eigenvalues. We also suppose familiarity with the solution of simple differential equations. This material is ordinarily covered in Math 234.

Homework Policy: Homework will be assigned in each class meeting except for testing days and should be done before the next class meeting. You are encouraged to work together on homework and ask for help on those problems that you do not understand. Homework will be collected and checked every Wednesday. No late homework will be accepted for any reason. When doing your homework, you should neatly show your work, one step under the other, with good work habits. You will learn the most by actively working exercises.

Examinations: Attendance at the scheduled examinations and final exam is required. There is no provision for absence due to vacations, family outings and other social activities, other special plans and appointments, etc. Absence due to illness require a medical excuse on Physician's letterhead, signed by the physician, which must be submitted before any alternate arrangements for the exam will be considered. All exams are closed book, closed notes. Calculators are not allowed or required on any exam. Outside of exams, I encourage you to use mathematics software and graphing calculators to improve your intuition.