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... PageRank may not reflect the true importance of the pages. – In some existing applications, the assumptions in existing algorithms may not be accurate either. Take importance calculation with the user browsing graph in BrowseRank (Liu et al. 2008) as an example. Basically BrowseRank trusts the user ...
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Hypothesis Tests - Kosuke Imai

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... Let an be the recursive relation defined by an = an–1 + an–2 + an–3, n > 3 with initial conditions : a0 = 1, a1 = 1, a2 = 1 (a) Obtain first few terms of recursive relation. (b) Prove that all an,s are odd. (c) Prove that an < 2n–1 ...
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... supply dumps of aircraft and motor vehicle tires captured in North Africa. The marking on each tire contained the maker’s name, a serial number, and a two-letter code for the date of manufacture. – The first step in analyzing the tire markings involved breaking the two-letter date code. • It was con ...
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Applied Statistics in Occupational Safety and Health

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Statistics - cengage.com.cn

... or chi-square to be skipped if desired with no loss in course coherence. A “Using Software” section near the end of each chapter makes it easy for instructors to emphasize the use of software in the course, or choose not to do so. • Examples using real data--Hundreds of well-chosen examples, based ...
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Preprint - Society for Industrial and Applied Mathematics

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... (a) The collection of good movies is not a well-defined set since the answer to the question: “Is Les Miserables a good movie?” may be subject to dispute. (b) This collection is a well-defined set since a person is either left-handed or right-handed. Of course, we are ignoring those few who can use ...
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Probability Theory and Statistics

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... might as well be Greek. It would be easier if it were Greek. We have very particular ideas about what is lacking here. In our experience, the problem stems from two deficiencies: 1. Humanists without training in the formal notation of mathematics—notation which in nearly every case values concision o ...
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My Stat 411 notes - University of Illinois at Chicago

... To understand the goal a bit better, let’s start with some notation. Let X1 , . . . , Xn be a random sample (independent and identically distributed, iid) from a distribution with cumulative distribution function (CDF) F (x). The CDF admits a probability mass function (PMF) in the discrete case and ...
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Probability on Graphs - Statistical Laboratory

... Interacting particle systems form the basis of Chapter 10. This is a large field in its own right, and little is done here beyond introductions to the contact, voter, exclusion models, and the stochastic Ising model. Chapter 11 is devoted to random graphs of Erd ős–Rényi type. There are accounts o ...
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... cannot be justified, a natural way to generalise the analysis is to model it as a renewal process. The renewal theorem provides asymptotic results for the first and second moment of the number of failures. For discretetime and continuous-time renewal processes, see Feller (1949, 1950) and Smith (195 ...
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Inequalities, Small Ball Probabilities and Applications

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Achievement - Western Springs College

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Expected Value and Variance - DIM

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Lists, Decisions and Graphs Edward A. Bender S. Gill Williamson

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Probability

Probability is the measure of the likeliness that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain we are that the event will occur. A simple example is the toss of a fair (unbiased) coin. Since the two outcomes are equally probable, the probability of ""heads"" equals the probability of ""tails"", so the probability is 1/2 (or 50%) chance of either ""heads"" or ""tails"".These concepts have been given an axiomatic mathematical formalization in probability theory (see probability axioms), which is used widely in such areas of study as mathematics, statistics, finance, gambling, science (in particular physics), artificial intelligence/machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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