Basic probability theory

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  • This is the first in a series of short books on probability theory and random processes for biomedical engineers. This text is written as an introduction to probability theory. The goal was to prepare students, engineers and scientists at all levels of background and experience for the application of this theory to a wide variety of problems—as well as pursue these topics at a more advanced level. The approach is to present a unified treatment of the subject. There are only a few key concepts involved in the basic theory of probability theory.

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  • Finance has become increasingly more quantitative, drawing on techniques in probability and statistics that many finance practitioners have not had exposure to before. In order to keep up, you need a firm understanding of this discipline. Probability and Statistics for Finance addresses this issue by showing you how to apply quantitative methods to portfolios, and in all matter of your practices, in a clear, concise manner. Informative and accessible, this guide starts off with the basics and builds to an intermediate level of mastery. ...

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  • This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory.

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  • This is an undergraduate course in digital communications, which is designed to prepare students for engineering work in high-tech industries and for graduate work in communications, signal processing, and computer systems. The course covers basic concepts and useful tools for design and performance analysis of transmitters and receivers in the physical layer of a communication system. Prerequisite: An introductory course in probability. A course in signals and systems. Texts: J.G. Proakis, M. Salehi, Communication Systems Engineering M. P. Fitz, A Course in Communication Theory Graders:...

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  • Lecture Monte carlo simulations: Application to lattice models, part I - Basics. The main contents of this chapter include all of the following: Introduction, thermodynamics and statistical mechanics, phase transition, probability theory.

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  • This volume describes the essential tools and techniques of statistical signal processing. At every stage, theoretical ideas are linked to specific applications in communications and signal processing. The book begins with an overview of basic probability, random objects, expectation, and second-order moment theory, followed by a wide variety of examples of the most popular random process models and their basic uses and properties.

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  • This compendium aims at providing a comprehensive overview of the main topics that appear in any well-structured course sequence in statistics for business and economics at the undergraduate and MBA levels. The idea is to supplement either formal or informal statistic textbooks such as, e.g., “Basic Statistical Ideas for Managers” by D.K. Hildebrand and R.L. Ott and “The Practice of Business Statistics: Using Data for Decisions” by D.S. Moore, G.P. McCabe, W.M. Duckworth and S.L. Sclove, with a summary of theory as well as with a couple of extra examples.

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  • This work gives an overview of core topics in the “investment” side of finance, stressing the quantitative aspects of the subject. The presentation is at a moderately sophisticated level that would be appropriate for masters or early doctoral students in economics, engineering, finance, and mathematics. It would also be suitable for advanced and well motivated undergraduates-provided they are adequately prepared in math, probability, and statistics.

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  • This book is intended to serve as the textbook for a …rst-year graduate course in econometrics. It can be used as a stand-alone text, or be used as a supplement to another text. Students are assumed to have an understanding of multivariate calculus, probability theory, linear algebra, and mathematical statistics. A prior course in undergraduate econometrics would be helpful, but not required. For reference, some of the basic tools of matrix algebra, probability, and statistics are reviewed in the Appendix....

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  • C H A P T E R 13 Smooth running – continuous probability distributions and basic queuing theory Chapter objectives This chapter will help you to: ■ ■ ■ ■ ■ ■ make use of the normal distribution and appreciate its importance employ the Standard Normal Distribution to investigate normal distribution problems apply the exponential distribution and be aware of its usefulness in analysing queues analyse a simple queuing system use the technology: continuous probability distribution become acquainted with business uses of the normal distribution...

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  • This compendium aims at providing a comprehensive overview of the main topics that appear in any well-structured course sequence in statistics for business and economics at the undergraduate and MBA levels. The idea is to supplement either formal or informal statistic textbooks such as, e.g., “Basic Statistical Ideas for Managers” by D.K. Hildebrand and R.L. Ott and “The Practice of Business Statistics: Using Data for Decisions” by D.S. Moore, G.P. McCabe, W.M. Duckworth and S.L. Sclove, with a summary of theory as well as with a couple of extra examples.

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  • This chapter is a collection of basic material on probability theory, information theory, complexity theory, number theory, abstract algebra, and finite fields that will be used throughout this book. Further background and proofs of the facts presented here can be found in the references given in x2.7. The following standard notation will be used throughout:

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  • MATHEMATICAL PRELIMINARIES Independent Component Analysis. Aapo Hyv¨ rinen, Juha Karhunen, Erkki Oja a Copyright  2001 John Wiley & Sons, Inc. ISBNs: 0-471-40540-X (Hardback); 0-471-22131-7 (Electronic) 2 Random Vectors and Independence In this chapter, we review central concepts of probability theory,statistics, and random processes. The emphasis is on multivariate statistics and random vectors. Matters that will be needed later in this book are discussed in more detail, including, for example, statistical independence and higher-order statistics.

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  • In this chapter, we study the mathematical structure of a simple one-period model of a financial market. We consider a finite number of assets. Their initial prices at time t = 0 are known, their future prices at time t = 1 are described as random variables on some probability space. Trading takes place at time t = 0. Already in this simple model, some basic principles of mathematical finance appear very clearly. In Section 1.2, we single out those models which satisfy a condition of market efficiency: There are no trading opportunities which yield a profit without any downside risk.

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  • Most raw ingredients will be labelled in bags, boxes or jars if in shipments, warehouses or in storerooms of pharmacies and retail outlets. The first step to identifying an ingredient is to compare the Roman, pinyin and/or Chinese characters to the name list in this guide. It is a matter of comparison and familiarisation with the characters and pinyin. If raw ingredients are not labelled and not obviously of interest (such as an animal horn or bones), it is best to refer to an expert or accept that identification is probably not possible.

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  • The purpose of this and the following chapter is to briefly go through the most basic concepts in probability theory and statistics that are important for you to understand. If these concepts are new to you, you should make sure that you have an intuitive feeling of their meaning before you move on to the following chapters in this book.

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  • When managers make choices or decisions under risk or uncertainty, they must somehow incorporate this risk into their decision-making process. This chapter presented some basic rules for managers to help them make decisions under conditions of risk and uncertainty. Conditions of risk occur when a manager must make a decision for which the outcome is not known with certainty.

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  • This book is targeted at programmers who need to develop solutions using XML. Being a programmer myself, I know that theory without practical examples and applications can be tedious, and you probably want to get straight to real-world examples. You’re in luck, because this book is full of working examples—but not in this chapter. Some theory is necessary so that you have a fundamental understanding of XML. I’ll keep the theory of XML and related technologies to a minimum as I progress through the chapters, but we do need to cover some of the basics up front....

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  • Bayesian Estimation Theory: Basic Definitions Bayesian Estimation The Estimate–Maximise Method Cramer–Rao Bound on the Minimum Estimator Variance Design of Mixture Gaussian Models Bayesian Classification Modeling the Space of a Random Process Summary B ayesian estimation is a framework for the formulation of statistical inference problems. In the prediction or estimation of a random process from a related observation signal, the Bayesian philosophy is based on combining the evidence contained in the signal with prior knowledge of the probability distribution of the process.

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