Basics of probability theory

Part 1 of ebook "Stochastic processes and calculus: An elementary introduction with applications" provides readers with contents including: Chapter 1 - Introduction; Chapter 2 - Basic concepts from probability theory; Chapter 3 - Autoregressive moving average processes (ARMA); Chapter 4 - Spectra of stationary processes; Chapter 5 - Long memory and fractional integration; Chapter 6 - Processes with autoregressive conditional heteroskedasticity (ARCH);...

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Cryptography is concerned with the conceptualization, definition, and construction of computing systems that address security concerns. The design of cryptographic systems must be based on firm foundations. This book presents a rigorous and systematic treatment of the foundational issues: defining cryptographic tasks and solving new cryptographic problems using existing tools. It focuses on the basic mathematical tools: computational difficulty (one-way functions), pseudorandomness, and zero-knowledge proofs.

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In this book you will find the basics of probability theory and statistics. In addition, there are several topics that go somewhat beyond the basics but that ought to be present in an introductory course: simulation, the Poisson process, the law of large numbers, and the central limit theorem. Computers have brought many changes in statistics. In particular, the bootstrap has earned its place. It provides the possibility to derive confidence intervals and perform tests of hypotheses where traditional (normal approximation or large sample) methods are inappropriate.

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This book presents the basic concepts of probability in a simple, straightforward, easy-to-understand way. It does require, however, a knowledge of arithmetic (fractions, decimals, and percents) and a knowledge of basic algebra (formulas, exponents, order of operations, etc.). If you need a review of these concepts, you can consult another of my books in this series entitled Pre-Algebra Demystified.

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Probability and Computer science - Lecture 1: Introduction to probability. This lecture provides students with content including: mathematical tools to deal with uncertain events; applications include; combinatorial analysis; counting; axioms of probability; conditional probability and inference;... Please refer to the detailed content of the lecture!

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The skill to solve mathematical problems facilitates students to develop their basic skills to solve problems in daily life. This study analyzes students' problem-solving process with a reflective cognitive style in constructing probability problems using action, process, object, and schema theory (APOS).

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During the years that I've been preparing Volume 4, I've often run across basic techniques of probability theory that I would have put into Section 1.2 of Volume 1 if I'd been clairvoyant enough to anticipate them in the 1960s. Finally I realized that I ought to collect most of them together in one place, near the beginning of Volume 4B, because the story of these developments is too interesting to be broken up into little pieces scattered here and there.

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Part 1 book "The feynman lectures on physics (Vol 1)" includes contents: Atoms in motion, basic physics, the relation of physics to other sciences, conservation of energy, time and distance, probability, the theory of gravitation, motion, Newton's laws of dynamics, conservation of momentum, vectors, characteristics of force, work and potential energy (a), work and potential energy (conclusion), the special theory of relativity, relativistic energy and momentum, space time, rotation in two dimensions,... and other contents.

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Part 1 of ebook "Basic radar analysis" provides readers with contents including: radar basics; radar range equation; radar cross section; noise; radar losses; detection theory; matched filter; detection probability improvement techniques; ambiguity function; waveform coding;...

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Part 1 of ebook "Statistics for business" provides readers with contents including: presenting and organizing data; characterizing and defining data; basic probability and counting rules; probability analysis for discrete data; probability analysis in the normal distribution; theory and methods of statistical sampling; estimating population characteristics;...

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Ebook Mathematical statistics: Basic ideas and selected topics (2nd, Vol 1): Part 2 presents the following content: Chapter 5 - asymptotic approximations, chapter 6 - inteference in the multiparameter case, appendix A - A review of basic probability theory, appendix B - Additional topics in probability and analysis, appendix C – Tables.

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Ebook Costing and quantitative techniques: Part 2 presents the following content: Chapter 10 cost data for short-run tactical decision making, chapter 11 cost control, chapter 12 cost ledger accounts, chapter 13 theory of index numbers, chapter 14 basic probability concepts, chapter 15 set theory, chapter 16 introduction to matrices, chapter 17 basic concepts of differentiation, chapter 18 basic linear programming, chapter 19 network analysis, chapter 20 replacement analysis, chapter 21 transportation model, chapter 22 computer assisted costing techniques.

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Part 1 of ebook "Mathematical statistics for economics and business" provide readers with content about: elements of probability theory; random variables, densities, and cumulative distribution functions; expectations and moments of random variables; parametric families of density functions; basic asymptotics; sampling, sample moments and sampling distributions;...

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Lecture Introduction to Machine learning and Data mining: Lesson 9.1. This lesson provides students with content about: probabilistic modeling; key concepts; application to classification and clustering; measurement uncertainty; basics of probability theory;... Please refer to the detailed content of the lecture!

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Part 1 of book "Introduction to machine learning" provide with knowledge about: a taste of machine learning; probability theory; basic algorithms; density estimation; limit theorems; panzer windows; exponential families; maximum likelihood estimation;...

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Probability theory deals with the study of random phenomena, which under repeated experiments yield different outcomes that have certain underlying patterns about them. The notion of an experiment assumes a set of repeatable conditions that allow any number of identical repetitions. After studying this chapter you will be able to understand: Axioms of Probability, conditional probability and independence, properties of conditional probability.

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Lecture Making hard decisions with the decision tool suite (3e) - Chapter 7: Probability basics. After completing this section, you will understand the knowledge about the basics of probability theory. Since uncertainty is a typical aspect of problems, rigorous and accurate problem solving requires using probability theory (i.e., math and logic). Specifically, we want you to: understand probability concepts, use probability to model simple situations, interpret probability statements, manipulate and analyze models,...

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(bq) the book is intended for a senior/graduate level course in probability and is aimed at students in electrical engineering, math, and physics departments. the authors' approach is to develop the subject of probability theory and stochastic processes as a deductive discipline and to illustrate the theory with basic applications of engineering interest.

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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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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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