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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
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Data Summary
Probability Axioms
Counting Strategies
Conditional Probability
Independence
Bayes’ Theorem
Discrete Random Variables
Expectation
Parameters
The Bernoulli Distribution
The Binomial Distribution
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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