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THE UNIVERSITY OF THE WEST INDIES DEPARTMENT OF ECONOMICS ECON3031: PROBABILITY AND DISTRIBUTION THEORY Semester 1, 2014-15 Pre-requisites: ECON 2008, ECON 1006 or MATH 1150 or MATH 1180 Anti-requisites: MATH 2140 Lecturer: Mr. Fabian Vassel Course Objectives: The course is aimed at: o Providing students with a formal treatment of probability theory. o Equipping students with essential tools for statistical analyses at the graduate level. o Fostering understanding through real-world statistical applications. Course Description: The course explores the basic concepts of modern probability theory and its applications for decision-making in economics, business, and other fields of social sciences. Our everyday lives, as well as economic and business activities, are full of uncertainties and probability and distribution theory offer useful techniques for quantifying these uncertainties. The course is heavily oriented towards the formulation of mathematical concepts on probability and probability distributions and densities with practical applications. Learning Outcomes At the end of the course students should be able to: o Develop problem-solving techniques needed to accurately calculate probabilities. o Apply problem-solving techniques to solving real-world events. o Apply selected probability distributions to solve problems. o Present the analysis of derived statistics to all audiences. Modes of Delivery There will be 1 hour of tutorial and 2 hours of lectures per week Assessment Mid-semester test: 30% Quiz: 20% Final Examination: 50% Syllabus 1. Probability Concepts o Definitions of probability o Axioms & Rules of Probability o Marginal, Joint & Conditional Probability o Bayes' Theorem II. Probability Distribution & Probability Density Functions o Discrete Random Variables & their Probability Distributions o Continuous Random Variables & their Probability Distributions o Bivariate and trivariate Distributions o Marginal & Conditional Distributions III. Mathematical Expectation o Expected Values of Random Variables o Moments & their Applications o Moment Generating Functions o Conditional expectation IV. Special Distributions o Special Discrete Probability Distribution Functions o Discrete Uniform o Bernoulli o Binomial o Poisson o Special Continuous Probability Distribution Functions o Continuous Uniform o Exponential Resources Prescribed: Miller, I. and Miller, Marylees. John E. Freund’s Mathematical Statistics with Application, 7th ed.,, New Jersey: Prentice Hall, 2010. Highly Recommended: Wackerly, D, Mendenhall, W. and Scheaffer, R. Mathematical Statistics with Applications. Duxbury: California, United States, 2008.