what is random

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What Is Random

Author : Edward Beltrami
ISBN : 9781461214724
Genre : Mathematics
File Size : 64. 53 MB
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In this fascinating book, mathematician Ed Beltrami takes a close enough look at randomness to make it mysteriously disappear. The results of coin tosses, it turns out, are determined from the start, and only our incomplete knowledge makes them look random. "Random" sequences of numbers are more elusive, but Godels undecidability theorem informs us that we will never know. Those familiar with quantum indeterminacy assert that order is an illusion, and that the world is fundamentally random. Yet randomness is also an illusion. Perhaps order and randomness, like waves and particles, are only two sides of the same (tossed) coin.

Random Vibration In Mechanical Systems

Author : Stephen H. Crandall
ISBN : 9781483269009
Genre : Technology & Engineering
File Size : 58. 52 MB
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Random Vibration in Mechanical Systems focuses on the fundamental facts and theories of random vibration in a form particularly applicable to mechanical engineers. The book first offers information on the characterization and transmission of random vibration. Discussions focus on the normal or Gaussian random process; excitation-response relations for stationary random processes; response of a single-degree-of-freedom system to stationary random excitation; wide-band and narrow-band random processes; and frequency decomposition of stationary random processes. The text then examines failure due to random vibration, including failure due to first excursion up to a certain level; fatigue failure due to a stationary narrow-band random stress process; failure due to an accumulation of damage; failure due to response remaining above a certain level for too great a fraction of the time; and failure mechanisms. The manuscript is a vital reference for mechanical engineers and researchers interested in random vibration in mechanical systems.

Random Fields Estimation

Author : Alexander G. Ramm
ISBN : 9789812565365
Genre : Technology & Engineering
File Size : 61. 30 MB
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This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory.This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory.

Mathematische Statistik

Author : Bartel L. van der Waerden
ISBN : 9783642649745
Genre : Mathematics
File Size : 82. 83 MB
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Der Kreative Zufall

Author : Klaus Mainzer
ISBN : 3406554288
Genre : Chance
File Size : 49. 37 MB
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Random Factors In Anova

Author : Sally Jackson
ISBN : 9781452206509
Genre : Social Science
File Size : 64. 55 MB
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When using the analysis of variance (ANOVA) in an experimental design, how can the researcher determine whether to treat a factor as fixed or random? This book provides the reader with the criteria to make the distinction between fixed and random levels among factors, an important decision that directly reflects the purpose of the research. In addition to exploring the varied roles random factors can play in social research, the authors provide a discussion of the statistical analyses required with random factors and give an overview of computer-assisted analysis of random factor designs using SAS and SPSSX.

Information Theoretic Methods For Estimating Of Complicated Probability Distributions

Author : Zhi Zong
ISBN : 0080463851
Genre : Mathematics
File Size : 69. 29 MB
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Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory. Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC - density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC

Fundamentals Of Amorphous Solids

Author : Zbigniew H. Stachurski
ISBN : 9783527682195
Genre : Technology & Engineering
File Size : 27. 99 MB
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Long awaited, this textbook fills the gap for convincing concepts to describe amorphous solids. Adopting a unique approach, the author develops a framework that lays the foundations for a theory of amorphousness. He unravels the scientific mysteries surrounding the topic, replacing rather vague notions of amorphous materials as disordered crystalline solids with the well-founded concept of ideal amorphous solids. A classification of amorphous materials into inorganic glasses, organic glasses, glassy metallic alloys, and thin films sets the scene for the development of the model of ideal amorphous solids, based on topology- and statistics-governed rules of three-dimensional sphere packing, which leads to structures with no short, mid or long-range order. This general model is then concretized to the description of specific compounds in the four fundamental classes of amorphous solids, as well as amorphous polyethylene and poly(methyl)methacrylate, emphasizing its versatility and descriptive power. Finally, he includes example applications to indicate the abundance of amorphous materials in modern-day technology, thus illustrating the importance of a better understanding of their structure and properties. Equally ideal as supplementary reading in courses on crystallography, mineralogy, solid state physics, and materials science where amorphous materials have played only a minor role until now.

Handbook Of Acoustics

Author : Malcolm J. Crocker
ISBN : 047125293X
Genre : Science
File Size : 84. 80 MB
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Acoustical engineers, researchers, architects, and designers need a comprehensive, single-volume reference that provides quick and convenient access to important information, answers and questions on a broad spectrum of topics, and helps solve the toughest problems in acoustical design and engineering. The Handbook of Acoustics meets that need. It offers concise coverage of the science and engineering of acoustics and vibration. In more than 100 clearly written chapters, experts from around the world share their knowledge and expertise in topics ranging from basic aerodynamics and jet noise to acoustical signal processing, and from the interaction of fluid motion and sound to infrasound, ultrasonics, and quantum acoustics. Topics covered include: * General linear acoustics * Nonlinear acoustics and cavitation * Aeroacoustics and atmospheric sound * Mechanical vibrations and shock * Statistical methods in acoustics * Architectural acoustics * Physiological acoustics * Underwater sound * Ultrasonics, quantum acoustics, and physical aspects of sound * Noise: its effects and control * Acoustical signal processing * Psychological acoustics * Speech communication * Music and musical acoustics * Acoustical measurements and instrumentation * Transducers The Handbook of Acoustics belongs on the reference shelf of every engineer, architect, research scientist, or designer with a professional interest in the propagation, control, transmission, and effects of sound.

Introductory Econometrics A Modern Approach

Author : Jeffrey M. Wooldridge
ISBN : 9781305446380
Genre : Business & Economics
File Size : 54. 48 MB
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Discover how empirical researchers today actually think about and apply econometric methods with the practical, professional approach in Wooldridge's INTRODUCTORY ECONOMETRICS: A MODERN APPROACH, 6E. Unlike traditional books, this unique presentation demonstrates how econometrics has moved beyond just a set of abstract tools to become genuinely useful for answering questions in business, policy evaluation, and forecasting environments. INTRODUCTORY ECONOMETRICS is organized around the type of data being analyzed with a systematic approach that only introduces assumptions as they are needed. This makes the material easier to understand and, ultimately, leads to better econometric practices. Packed with timely, relevant applications, the book introduces the latest emerging developments in the field. Gain a full understanding of the impact of econometrics in real practice today with the insights and applications found only in INTRODUCTORY ECONOMETRICS: A MODERN APPROACH, 6E. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

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