- Demonstrate a working knowledge of the basic definitions of discrete and continuous
Markov chains, the Poisson process, Brownian motion and its preliminary stochastic
calculus.
- Be able to effectively utilize the computer package R to perform the basic calculations
required to apply the methods covered in the course, and to demonstrate the methods
using simulation.
- Be able to apply the methods covered in the course to a large variety of problems
one may encounter on actuarial exams.
- Appreciate how probability theory can be applied to the study of phenomena in fields
as diverse as engineering, computer science, management science, the physical and
social sciences, and operational research.
Current Textbook: Introduction to Probability Models (11th Ed.), Sheldon M. Ross, Academic Press, 2014.
| Topics Covered |
Chapters
|
Time |
| Review of Basic Probability: Events and random variables, permutations, combinations,
simulation, conditional probability, independence, common distributions and their
properties |
1-2-3
|
2.5 weeks |
| Discrete Markov chain theory: Chapman-Kolmogorov's equations, classification of states,
equilibrium and its applications, branching processes, MCMC methods |
4
|
3.5 weeks |
| Exponential distribution and Poisson processes: memoryless property, counting processes,
interarrival times, applications to insurance |
5
|
2.5 weeks |
| Continuous Markov models: Birth and Death processes, queueing models, limiting probabilities,
transition functions |
6
|
3 weeks |
| Rudiments of Brownian motion, stochastic integration, Gaussian time series analysis |
10
|
2.5 weeks |
The above textbook and course outline should correspond to the most recent offering
of the course by the Statistics Department. Please check the current course homepage
or with the instructor for the course regulations, expectations, and operating procedures.
Contact Faculty: David Hitchcock
|