OA3301 Stochastic Models I

Course objectives are to provide an introduction to stochastic modeling. Topics include the homogeneous Poisson process and its generalizations and discrete and continuous time Markov chains and their applications in modeling random phenomena in civilian and military problems.

Prerequisite

OA3101 or consent of instructor

Lecture Hours

4

Lab Hours

0

Course Learning Outcomes

·      Develop working knowledge about probability models—a mathematical model that involves uncertainty. Learn four methods to assess the expected value of a random variable: by definition, by summation, by conditioning, and by Monte Carlo simulation.

·      Use a discrete-time Markov chain to model a dynamic system that evolves over time. Understand the classification of states and how to analyze a Markov chain, including the limiting probabilities, the absorption probabilities, and the expected times to absorption.

·      Use a continuous random variable to model the lifetime of a component. Compute probability measures and expected values concerning a system’s lifetime that involves multiple components.

·      Understand conditional variance and use the conditioning technique to compute the variance of a random variable.

·      Understand the memoryless property of the exponential distribution and use this property
to compute probability measures and expected values for various quantities of interest.

·      Develop knowledge about counting processes, including the concepts of independent increments and stationary increments. Work with the Bernoulli processes and the Poisson processes and understand when it is appropriate to adopt them in a probability model.