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concise.notes

concise.notes - IE230 CONCISE NOTES Revised January 9 2011...

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IE230 C ONCISE N OTES Revised January 9, 2011 Purpose: These concise notes contain the definitions and results for Purdue University’s course IE 230, "Probability and Statistics for Engineers, I". The purpose of these notes is to provide a complete, clear, and concise compendium. The purpose of the lectures, textbook, homework assignments, and office hours is to help understand the meanings and implications of these notes via discussion and examples. Essentially everything here is in Chapters 2–7 of the textbook, often in the highlighted blue boxes. Topic order roughly follows the textbook. Textbook: D.C. Montgomery and G.C. Runger, Applied Statistics and Probability for Engineers , John Wiley & Sons, New York, 2007 (fourth edition). Table of Contents Topic Pages Textbook Set-Theory Review 2 None Probability Basics 3–5 Chapter 2 sample space and events 3 event probability 4 conditional probability, independence 5 Discrete Random Variables 6–8 Chapter 3 pmf, cdf, moments 6 uniform, Bernoulli trials, Poisson process 7 summary table: discrete distributions 8 Continuous Random Variables 9–12 Chapter 4 pdf, cdf, moments, uniform, triangular 9 normal distribution, central limit theorem 10 normal approximations, continuity correction 11 exponential, Erlang, gamma, Weibull 11 Chebyshev’s inequality 11 None summary table: continuous distributions 12 Random Vectors 13–18 Chapter 5 discrete joint and marginal distributions 13 conditional distributions 14 multinomial distribution 14 continuous distributions 15 conditional distributions 16 covariance, correlation 17 bivariate normal 17 linear combinations, sample mean, central limit theorem 18 Descriptive Statistics 19 Chapter 6 Point Estimation 20–22 Chapter 7 parameter estimator and their properties 20 summary table: point estimators, sampling distribution 21 fitting distributions, MOM, MLE 22 Purdue University – 1 of 22 – B.W. Schmeiser

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IE230 C ONCISE N OTES Revised January 9, 2011 Set-Theory Review A set is a collection of items; each such item is called a member of the set. If a set A has members x , y , and z , we can write A = { x , y , z } and, for example, x A . If a set has members defined by a condition, we write A = { x | x satisfies the condition} . The vertical line is read "such that". The largest set is the universe , the set containing all relevant items. The smallest set is the empty set (or, sometimes, the null set ), the set containing no items; it is denoted by or, occasionally, by {} . If all members of a set A are contained in a set B , then A is a subset of B , written A B . If two sets A and B contain the same members, then they are equal, written A = B . The union of two sets A and B is the set of items contained in at least one of the sets; that is, A B = { x | x A or x B } . The intersection of two sets A and B is the set of items contained in both sets; that is, A B = { x | x A and x B } . This intersection is also written AB .
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concise.notes - IE230 CONCISE NOTES Revised January 9 2011...

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