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University of Vermont Department of Mathematics and Statistics Course: STAT 151 Spring 2014 Course Description Applied Probability is an introductory course designed to provide students with an appreciation for stochastic explanations of natural phenomena. The notion of probability will be developed from an experimental as well as a theoretical perspective. The student will learn to recognize appropriate conceptual models when confronted with a problem, and be able to select and apply suitable mathematical techniques to compute expectations and event probabilities. Examples and exercises will focus on a variety of applications including actuarial science, engineering, medicine, and business. A prior working knowledge of the material covered in the first two semesters of calculus, including integration, is an essential prerequisite. Topics Covered o o o o o o o o o o o Data Summary Probability Axioms Counting Strategies Conditional Probability Independence Bayesâ€™ Theorem Discrete Random Variables Expectation Parameters The Bernoulli Distribution The Binomial Distribution o o o o o o o o o o o The Poisson Distribution Moment-Generating Functions Continuous Data Continuous Random Variables The Uniform Distribution The Exponential Distribution The Gamma Distribution The Chi-Square Distribution The Normal Distribution Bivariate Distributions Conditional Distributions Course Textbook Robert V. Hogg and Elliot A. Tanis. Probability and Statistical Inference ( 8th Edition). Prentice Hall. Upper Saddle River, NJ, 2010. ISBN: 978-0321-584-755