- 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.
|Review of Basic Probability: Events and random variables, permutations, combinations, simulation, conditional probability, independence, common distributions and their properties
|Discrete Markov chain theory: Chapman-Kolmogorov's equations, classification of states, equilibrium and its applications, branching processes, MCMC methods
|Exponential distribution and Poisson processes: memoryless property, counting processes, interarrival times, applications to insurance
|Continuous Markov models: Birth and Death processes, queueing models, limiting probabilities, transition functions
|Rudiments of Brownian motion, stochastic integration, Gaussian time series analysis
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: Paramita Chakraborty