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Probability and Statistics: Students
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Probability and Statistics are as much about intuition and problem solving as they are about theorem proving. Because of this, students can find it very difficult to make a successful transition from lectures to examinations to practice, since the problems involved can vary so much in nature. Since the subject is critical in many modern applications such as mathematical finance, quantitative management, telecommunications, signal processing, bioinformatics, as well as traditional ones such as insurance, social science andengineering, the authors have rectified deficiencies in traditional lecture-based methods by collecting together a wealth of exercises with complete solutions, adapted to needs and skills of students. Following on from the success of Probability and Statistics by Example: Basic Probability and Statistics, the authors here concentrate on random processes, particularly Markov processes, emphasising modelsrather than general constructions. Basic mathematical facts are supplied as and when they are needed andhistorical information is sprinkled throughout.
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Probability and Statistics are the mathematics used to understand chance and to collect, organize, describe, and analyze numerical data. From weather reports to sophisticated studies of genetics, from election results to product preference survey, probability and statistical language and concepts are increasingly present in the media and in everyday conversations. Students need this mathematics to help them judge the correctness of an argument supported by seemingly persuasive data.
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Probability & Statistics was written for a one or two semester probability and statistics course offered primarily at four-year institutions and taken mostly by sophomore and junior level students, majoring in mathematics or statistics. Calculus is a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus. The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a new chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), expanded coverage of residual analysis in linear models, and more examples using real data.
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By the end of the course students will be sensible, critical users of probability and statistics, able to apply the processes and principles developed in this course to real-world problems. Students should not think that those people who did not win the lottery yesterday have a greater chance of winning today! They should not believe an argument merely because various statistics are offered. Rather, they should be able to judge whether the statistics are meaningful and are being used appropriately.
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The Department of Mathematics and Statistics is pleased to host a one day conference on Probability and Statistics on Saturday, April 28, 2007. This will be a full day event with Keynote addresses by two prominent statisticians. Plenary sessions, contributed sessions, and oral and poster presentations by graduate students are ... planned.
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Introduction to Probability Probability defines the concepts of probability spaces, random variables, distributions, density and distribution functions. Independent and IID (independent identically distributed) random variables are ... discussed. It ends with the introduction of expected values, attempting to provide an introduction that is accessible to a student who has not quite yet had a course in calculus.
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