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Topic: Probability theory

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  Probability Theory - The Laymans guide to probability   (Site not responding. Last check: 2007-10-25)
The probability of throwing a double three with two dice is the result of throwing three with the first die and three with the second die.
For example, The probability of throwing a 1 on a die is 1/6 therefore the probability of a 'non-1' is (1-1/6) which equals 5/6.
The theory of probability becomes of enhanced value to gamblers when it is used with the law of large numbers.
www.probabilitytheory.info - http: //www.peterwebb.co.uk/probability.htm   (6661 words)

  Probability - Wikipedia, the free encyclopedia
In Cox's formulation, probability is taken as a primitive (that is, not further analyzed) and the emphasis is on constructing a consistent assignment of probability values to propositions.
Probabilities are equivalently expressed as odds, which is the ratio of the probability of one event to the probability of all other events.
Governments typically apply probability methods in environment regulation where it is called "pathway analysis", and are often measuring well-being using methods that are stochastic in nature, and choosing projects to undertake based on their perceived probable effect on the population as a whole, statistically.
en.wikipedia.org /wiki/Probability   (2730 words)

 math lessons - Probability theory
Probability theory is the mathematical study of probability.
Probabilities P(E) are assigned to events E according to the probability axioms.
Others assign probabilities to propositions that are uncertain according either to subjective degrees of belief in their truth, or to logically justifiable degrees of belief in their truth.
www.mathdaily.com /lessons/Probability_theory   (754 words)

 Probability, Distributions
Without probability theory, there would be no way to describe the way samples might differ from the populations from which they were drawn.
The probability of an event E, P(E), is the proportion of times the event occurs in a long series of experiments.
The probability that something is true for an individual selected at random from a population is equal to the fraction of the population for whom it is true.
www.tufts.edu /~gdallal/prob.htm   (884 words)

The probability of landing on blue is one fourth.
The probability of landing on each color of the spinner is always one fourth.
The probability of an event is the measure of the chance that the event will occur as a result of an experiment.
www.mathgoodies.com /lessons/vol6/intro_probability.html   (783 words)

 Probability Theory - The Laymans guide to probability   (Site not responding. Last check: 2007-10-25)
The probability of throwing a double three with two dice is the result of throwing three with the first die and three with the second die.
For example, The probability of throwing a 1 on a die is 1/6 therefore the probability of a 'non-1' is (1-1/6) which equals 5/6.
The theory of probability becomes of enhanced value to gamblers when it is used with the law of large numbers.
www.probabilitytheory.info - !http: //www.peterwebb.co.uk/probability.htm   (6661 words)

 Statistics Glossary - probability
Probability is conventionally expressed on a scale from 0 to 1; a rare event has a probability close to 0, a very common event has a probability close to 1.
Like all probabilities, a subjective probability is conventionally expressed on a scale from 0 to 1; a rare event has a subjective probability close to 0, a very common event has a subjective probability close to 1.
In probability theory we say that two events, A and B, are independent if the probability that they both occur is equal to the product of the probabilities of the two individual events, i.e.
www.stats.gla.ac.uk /steps/glossary/probability.html   (1632 words)

 probability theory --  Encyclopædia Britannica
Probability has its origin in the study of gambling and insurance in the 17th century, and it is now an indispensable tool of both social and natural sciences.
His original contributions to the fields of probability theory and topology have had a significant impact on modern physics, chemistry, biology, and cybernetics.
Jakob (1654–1705), a professor of mathematics at the University of Basel, is best known for his work on the theory of probability and his principles of the calculus of variation.
www.britannica.com /eb/article-9109439   (884 words)

 Quantum Logic and Probability Theory (Stanford Encyclopedia of Philosophy)
Mackey presents a sequence of six axioms, framing a very conservative generalized probability theory, that underwrite the construction of a ‘logic’ of experimental propositions, or, in his terminology, ‘questions’, having the structure of a sigma-orthomodular poset.
Thus, a state is a consistent assignment of a probability weight to each test -- consistent in that, where two distinct tests share a common outcome, the state assigns that outcome the same probability whether it is secured as a result of one test or the other.
In classical probability theory (and especially in classical statistics) one usually focuses, not on the set of all possible probability weights, but on some designated subset of these (e.g., those belonging to a given family of distributions).
plato.stanford.edu /entries/qt-quantlog   (8000 words)

There are other domains, most notably measure theory, where the same rules appear, but from the point of view of learning systems and decisions in the face of uncertainty, degree of belief is the appropriate interpretation.
In particular, under the belief interpretation probability is not an objective property of some physical setting, but is conditional to the prior assumptions and experience of the learning system.
It is completely reasonable to talk about ``the probability that there is a tenth planet in the solar system'' although this planet either exists or does not exist and there is no sense in interpreting the probability as a frequency of observing a tenth planet.
www.cis.hut.fi /harri/thesis/valpola_thesis/node12.html   (224 words)

 Rigorous Probability Theory
This textbook is an introduction to probability theory using measure theory.
Theory") and found it to be an excellent book for review and remediation--that is, it helped me get a better overview of the material I had already learned and it helped me learn topics such as, say, uniform integrability, that didn't sink in too well the first time around.
Furthermore, the measure theory is almost always discussed purely in terms of probability, as opposed to being treated as a separate subject which must be mastered before probability theory can be studied.
probability.ca /jeff/grprobbook.html   (1619 words)

 probability theory
While mathematicians agree on how to calculate the probability of certain events and how to use those calculations in certain ways, there's plenty of disagreement as to what the numbers actually mean.
The latter, for example, is what we're talking about when we say that it's "probable" that a certain suspect committed a crime based on the available evidence.
It is an open question whether aleatory probability is reducible to epistemic probability based on our inability to precisely predict every force that might affect the roll of a die, or whether such uncertainties exist in the nature of reality itself, particularly at the level of quantum mechanics.
www.daviddarling.info /encyclopedia/P/probability_theory.html   (199 words)

 Theory of Probability: Introduction, formulae, software, algorithms
Probability is defined as the rapport of the favorable cases over total cases, or calculated as: p = n / N. The probability can be also understood as expected number of successes in one trial.
The probability theory formula is also known as the probability of exactly M successes of K elements drawn in a pool of S favorable elements from a total of N elements.
The probability (odds) of separable events, multiple trials is another problem in theory of probability.
www.saliu.com /theory-of-probability.html   (4688 words)

 60: Probability theory and stochastic processes
Probability theory is simply enumerative combinatorial analysis when applied to finite sets; thus the techniques and results resemble those of discrete mathematics.
Probability concepts are applied across mathematics when considering random structures, and in particular lead to good algorithms in some settings even in pure mathematics.
Probability questions given a finite sample space are usually "just" a lot of counting, and so are included with combinatorics.
www.math.niu.edu /~rusin/known-math/index/60-XX.html   (855 words)

 Probability Theory
Probability Theory can be used in various forms for many different applications.
Probability is also central to the Genetic Methods.
Another application of Probability Theory occurs when uncertainties are determined for a set of predicted values or computational results such as expectation values.
members.aol.com /btluke/prob01.htm   (905 words)

 Probability Theory - Cambridge University Press
In this book, E. Jaynes dispels the imaginary distinction between ‘probability theory’ and ‘statistical inference’, leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications.
This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context.
New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology.
www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521592712   (351 words)

 Probability Theory As Extended Logic
Edwin T. Jaynes was one of the first people to realize that probability theory, as originated by Laplace, is a generalization of Aristotelian logic that reduces to deductive logic in the special case that our hypotheses are either true or false.
A typed publication quality version of his unpublished book titled "Probability Theory, With Applications in Science and Engineering" that was being prepared for publication in the mid 1970's is available.
These article are on the application of probability theory to the problem of estimating the frequency of oscillation of a non-sinusoidal signal in data that consists of counts.
bayes.wustl.edu   (681 words)

 Gambling Formula: Degree of Certainty, Probability, Mathematics, Chance
All lottery cases and data do confirm the theory of probability and the formula of bankruptcy...
the probability of getting one point face when rolling a die is '1 in 6' or p = 1/6; the probability of getting one roulette number is '1 in 38' or p = 1/38.
If the probability is 1/N and we repeat the event N times, the degree of certainty is {1 — (1/e)}, when N tends to infinity.
www.saliu.com /Saliu2.htm   (2846 words)

 Free probability theory   (Site not responding. Last check: 2007-10-25)
The workshop would bring together researchers specialized in free probability, and people who have interests in free probability but work primarily in some of the above mentioned related areas.
It has also turned out in recent years that free probability is quite attractive and promising for young people.
There are a lot of interesting problems on a level accesible to graduate students and postdoctoral fellows.
www.pims.math.ca /birs/workshops/2004/04w5028   (196 words)

 Probability Theory
, the probability of the desired outcomes is:
Join Probability: The probability of the desired outcomes is the sum of the probability of each event resulting in a desired outcome.
Both variance and standard deviation are used to describe the spread of a distribution.
www.efunda.com /math/probability/probability.cfm   (206 words)

 Wilmott | Serving The Quantitative Finance Community | Bookshop
Comprising the major theorems of probability theory and the measure theoretical foundations of the subject, the main topics treated here are independence, interchangeability, and martingales.
No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability.
It is easily adapted for graduate students familiar with measure theory using the guidelines given.
books.global-investor.com /books/21911.htm?ginPtrCode=10202   (256 words)

 Mathematics Archives - Topics in Mathematics - Probability
The Birthday Problem: A short lesson in probability
Front for the XXX Mathematics Archive - Probablility Theory
Collection of articles, Evaluating Probabilities of Boolean Events, The Gambler's Ruin, Area Under the Bell Curve, The Poisson Distribution and Queues, Ratio Populations, Ratios of Normal Distributions, Failure Rates, MTBFs, All That and Boolean Expansion as Linear Interpolation, etc.
archives.math.utk.edu /topics/probability.html   (487 words)

4-1 Chapter 5 Queer Uses for Probability Theory Chapter 6 Elementary Parameter Estimation Fig.
Appendix A Other Approaches to Probability Theory Appendix B Formalities and Mathematical Style Appendix C Convolutions and Cumulants Appendix D Dirichlet Integrals and Generating Functions Appendix E The Binomial -- Gaussian Hierarchy of Distributions Appendix F Fourier Analysis Appendix G Infinite Series Appendix H Matrix Analysis and Computation Appendix I Computer Programs
Probability Theory is Different COMMENTS Gamesmanship What Does `Bayesian' Mean?
omega.math.albany.edu:8008 /JaynesBook.html   (429 words)

 Probability Theory as Logic Reference List
I have set up this web page in order to make available to the DØ collaboration some papers I have found to useful in my study of probability theory.
This is an excellent introduction, covering everything from the definition of probability to examples of parameter estimation and model comparison.
Includes a critique of frequentist statistics, noting when and why it works, and when and why it fails.
d0server1.fnal.gov /users/paterno/public_html/probability   (838 words)

 Probability Theory
Gamblers were crafty enough to figure simple laws of probability by witnessing the events at first hand.
The opportunity was limitless in then exploiting the often complex and sometimes seemingly contradictory laws of probability.
I did so because a lot of people I spoke to had little knowledge of elementary probability and I spend hours arguing with them about pretty basic laws of probability.
www.probabilitytheory.info   (424 words)

 Probability Theory   (Site not responding. Last check: 2007-10-25)
FELLER W. (William), "An introduction to probability theory and its applications" Vols.
FELDMAN D. (Dorian), FOX M., "Probability: the mathematics of uncertainty" (1991).
FRISTEDT B. (Bert), GRAY L., "A modern approach to probability theory" (1996,1997).
www.math.tau.ac.il /~tsirel/Courses/Prob/syllabus.html   (202 words)

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