Measure theory provides a way to define a conditional probability, using the family of events R < sub > ab </ sub > =

) Measure spaces and probability spaces play a foundational role in measure theory and probability theory respectively.

* Measure ( mathematics ), a way to assign non-negative real numbers to subsets

* Measure ( physics ), a way to integrate over all possible histories of a system in quantum field theory

* Measure ( termination ), a way to describe termination of processes, algorithms, or functions

* Measure ( data warehouse ), a property on which calculations can be made using precomputed aggregates

* Measure ( typography ), in typography refers to the width of a block or column of text from the left margin to the right margin

* Measure ( album ), a 2000 album from Matt Pond PA

Examples of measures and measurement methods are Mean Opinion Score ( MOS ), Perceptual Speech Quality Measure ( PSQM ) and Perceptual Evaluation of Video Quality ( PEVQ ).

Other stage work at this time included The Night of the Ball ( New Theatre, 1955 ), the new Robert Bolt play Flowering Cherry ( Haymarket, 1958, Broadway, 1959 ), Toys in the Attic ( Piccadilly, 1960 ), The Wings of the Dove ( Lyric, 1963 ), A Measure of Cruelty ( Birmingham Repertory, 1965 ), A Present for the Past ( Edinburgh, 1966 ), The Sacred Flame ( Duke of York's Theatre, 1967 ) with Gladys Cooper, The Battle of Shrivings ( Lyric, 1970 ) with John Gielgud and Lies ( Albery, 1975 ).

Located in the Central Valley, Tracy sits near some fertile agricultural lands and some not so fertile agricultural lands ( because of the hilly region west of Tracy ), some of which ( in the east and mostly north of Tracy because of the moist Delta river system ) has come under increasing development pressure as the San Francisco Bay Area's vigorous population growth has spilled over into the Tracy area as well as other locations such as new town of Mountain House ( because of TRAQC's Measure A in 1990 ) near the Bay Area's edge.

He also had triumphs as Malvolio in Twelfth Night ( 1931 ), Shylock in The Merchant of Venice ( 1937 ), Angelo in Measure for Measure ( 1950 ), Cassius in Julius Caesar ( 1950 ) ( which he immortalised in the 1953 film ), Leontes in The Winter's Tale ( 1951 ), and Cardinal Wolsey in Henry VIII ( 1959 ) ( although his 1960 performance as Othello was not a success ).

It focuses on topics of particular relevance to women, such as care work or occupational segregation ( exclusion of women and minorities from certain fields ); deficiencies of economic models, such as disregarding intra-household bargaining ; new forms of data collection and measurement such as the Gender Empowerment Measure ( GEM ), and more gender-aware theories such as the capabilities approach.

In 1999 the group acknowledged their growing influences and their need to experiment with a double-album How to Measure a Planet ?.

* Coherence ( philosophical gambling strategy ), analogous concept in Bayesian probability

covers statistical study, descriptive statistics ( collection, description, analysis, and summary of data ), probability, and the binomial and normal distributions, test of hypotheses and confidence intervals, linear regression, and correlation.

* For the frequentist a hypothesis is a proposition ( which must be either true or false ), so that the frequentist probability of a hypothesis is either one or zero.

In probability theory and statistics, the cumulative distribution function ( CDF ), or just distribution function, describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x.

In a sense that can be made precise, the probability that two randomly chosen integers are coprime is 6 / π < sup > 2 </ sup > ( see pi ), which is about 61 %.

If a probability distribution has a density function f ( x ), then the mean is

* Conditioning ( probability ), a concept in probability theory

This method, widely used in drug development, is referred to as rNPV ( risk-adjusted NPV ), and similar methods are used to incorporate credit risk in the probability model of CDS valuation.

* Event ( probability theory ), a set of outcomes to which a probability is assigned

For example, in a system where there is no queuing, the GoS may be that no more than 1 call in 100 is blocked ( i. e., rejected ) due to all circuits being in use ( a GoS of 0. 01 ), which becomes the target probability of call blocking, P < sub > b </ sub >, when using the Erlang B formula.

Erlang-B ( sometimes also written without the hyphen Erlang B ), also known as the Erlang loss formula, is a formula for the blocking probability derived from the Erlang distribution to describe the probability of call loss on a group of circuits ( in a circuit switched network, or equivalent ).

In this case the probability that the gcd equals d is d < sup >− 2 </ sup >/ ζ ( 2 ), and since ζ ( 2 ) = π < sup > 2 </ sup >/ 6 we have

Since the probability of a run of five successive heads is only ( one in thirty-two ), a believer in the gambler's fallacy might believe that this next flip is less likely to be heads than to be tails.

By the time this reaches 5 losses ( 11 rolls left ), his probability of winning on one of the remaining rolls will have dropped to ~ 50 %.

While the Trivers – Willard hypothesis predicts that birth sex is dependent on living conditions ( i. e. more male children are born in " good " living conditions, while more female children are born in poorer living conditions ), the probability of having a child of either gender is still regarded as 50 / 50.

An upper limit of 750 BC is indicated by a number of considerations, such as the probability that his work was written down, the fact that he mentions a sanctuary at Delphi that was of little national significance before c. 750 BC ( Theogony l. 499 ), and he lists rivers that flow into the Euxine, a region explored and developed by Greek colonists beginning in the 8th century BC.

), and each input may independently occur with uniform probability, then a hash function need only map roughly the same number of inputs to each hash value.

There is also a strong probability that for most or all of the period the temple at Bethel in Benjamin replaced that at Jerusalem, boosting the prestige of Bethel's priests ( the Aaronites ) against those of Jerusalem ( the Zadokites ), now in exile in Babylon.

If these bits are known ahead of transmission ( to be a certain value with absolute probability ), logic dictates that no information has been transmitted.

The Kullback – Leibler divergence ( or information divergence, information gain, or relative entropy ) is a way of comparing two distributions: a " true " probability distribution p ( X ), and an arbitrary probability distribution q ( X ).

We devote a chapter to the binomial distribution not only because it is a mathematical model for an enormous variety of real life phenomena, but also because it has important properties that recur in many other probability models.

He used his time in Bourg to research mathematics, producing Considérations sur la théorie mathématique de jeu ( 1802 ; “ Considerations on the Mathematical Theory of Games ”), a treatise on mathematical probability that he sent to the Paris Academy of Sciences in 1803.

Classical physics draws a distinction between particles and energy, holding that only the latter exhibit waveform characteristics, whereas quantum mechanics is based on the observation that matter has both wave and particle aspects and postulates that the state of every subatomic particle can be described by a wavefunction — a mathematical expression used to calculate the probability that the particle, if measured, will be in a given location or state of motion.

One of the mathematical constructs that enables experimenters to predict very accurately certain experimental results is sometimes called a probability wave.

In its mathematical form it is analogous to the description of a physical wave, but its " crests " and " troughs " indicate levels of probability for the occurrence of certain phenomena ( e. g., a spark of light at a certain point on a detector screen ) that can be observed in the macro world of ordinary human experience.

The probability " wave " can be said to " pass through space " because the probability values that one can compute from its mathematical representation are dependent on time.

In probability theory, the expected value ( or expectation, or mathematical expectation, or mean, or the first moment ) of a random variable is the weighted average of all possible values that this random variable can take on.

As an interpretation, it is not in conflict with the mathematical axiomatization of probability theory ; rather, it provides guidance for how to apply mathematical probability theory to real-world situations.

He worked on a great variety of mathematical topics, including series, number theory, mathematical analysis, geometry, algebra, combinatorics, and probability.

In 1974, Young Earth Creationist Henry M. Morris introduced a similar concept in his book Scientific Creationism in which he wrote ; " This issue can actually be attacked quantitatively, using simple principles of mathematical probability.

The mathematical probability that resemblances are accidental decreases sharply with the number of languages concerned ( 1957: 39 ).

The film is based on Ben Mezrich's best seller, Bringing Down the House: The Inside Story of Six MIT Students Who Took Vegas for Millions, a story of student MIT card-counters who used mathematical probability to aid them in card games such as blackjack.

The concept has been given an axiomatic mathematical derivation in probability theory, which is used widely in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence / machine learning and philosophy to, for example, draw inferences about the expected frequency of events.

Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions arose much later.

Whereas games of chance provided the impetus for the mathematical study of probability, fundamental issues are still obscured by the superstitions of gamblers.

See Ian Hacking's The Emergence of Probability and James Franklin's The Science of Conjecture for histories of the early development of the very concept of mathematical probability.

The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance.

The philosophy of probability presents problems chiefly in matters of epistemology and the uneasy interface between mathematical concepts and ordinary language as it is used by non-mathematicians.

In its axiomatic form, mathematical statements about probability theory carry the same sort of epistemological confidence shared by other mathematical statements in the philosophy of mathematics.