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Axioms of probability
| Glossary of Statistical Terms |
There are three axioms of probability: (1) chances are always at least zero. (2) the chance that something happens is 100%. (3) if two events cannot both occur at the same time (if they are disjoint or mutually exclusive), the chance that either one occurs is the sum of the chances that each occurs. for example, consider an experiment that consists of tossing a coin once. the first axiom says that the chance that the coin lands heads, for instance, must be at least zero. the second axiom says that the chance that the coin either lands heads or lands tails or lands on its edge or doesn`t land at all is 100%. the third axiom says that the chance that the coin either lands heads or lands tails is the sum of the chance that the coin lands heads and the chance that the coin lands tails, because both cannot occur in the same coin toss. all other mathematical facts about probability can be derived from these three axioms. for example, it is true that the chance that an event does not occur is (100% − the chance that the event occurs). this is a consequence of the second and third axioms.
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Axiom, шведский
Axiom, английский
- A self-evident truth or proposition, that cannot be made plainer by demonstration.
- Аксиома
- An axiom is a sentence, or relation, in a logic system that is assumed to be true. some familiar examples would be the axioms of euclidan geometry or kolmogorov`s axioms of probability. a more prosaic example would be the axiom that "all animals have a mother and a father" in a genetics tracking system (e.g., boblo). see also: assertion, boblo.
Axiom of assignment, английский
Аксиома присваивания
Axiom of choice, английский
Аксиома выбора
Axiom of iteration, английский
Аксиома цикла
Axiom of selection, английский
Аксиома выбора
Axiom scheme, английский
Схема аксиом
Axioma, atis, n, латинский
Axiomatic, английский
Аксиоматический; очевидный
Axiomatic approach, английский
Аксиоматический подход
Axiomatic definition, английский
Аксиоматическое определение
Axiomatic semantics, английский
Аксиоматическая семантика
Axiomatics, английский
Аксиоматика
Axiometer, английский
Probability, английский
- Probability can be generally defined as a measure of how likely some event will occur. the event could be an explosion, a lottery win or perhaps cancer induction. mathematically speaking, the value of probability varies between 0 and 1 where 0 means an ev
- Вероятность. возможность.
- The probability of an event is a number between zero and 100%. the meaning (interpretation) of probability is the subject of theories of probability, which differ in their interpretations. however, any rule for assigning probabilities to events has to satisfy the axioms of probability.
- Вероятность
- Вероятность probability sample, syn. random sample
- Вероятность. мера случайности появления конкретного события. например, вероятность случайного выбора из популяции человека с конкретным качеством соответствует доле людей в популяции, обладающих этим качеством.
- Вероятность; возможность
- Вероятность; обеспеченность (гидрологической величины) ~ of no-failure вероятность безотказной работы
- Probability is a method for representing uncertainty about propositions or events. it represents the uncertainty about a proposition on a scale from 0 to 1, with a 0 representing complete certainty that the proposition is false or an event will not occur and a value of one will represent the opposite. formally, a probability measure is one that follows kolmogorov`s axioms. there are two main schools of thought on the meaning of probability. frequentists take a narrow interpretation of probability allowing only hypothetically repeatable events or experiments as being quantifiable by probability, while bayesians take a broader interpretation that allows reasoning about "one-shot" events and propositions based on the current knowledge about nature. the bayesian interpretation is most commonly used in artificial intelligence, while the frequentist interpretation is most commonly taught in statistics courses. the label "bayesian" arises from the central role that the bayes theorem plays in this use of probability. it allows one to reason from effects to causes and encourages the use of probability measures to describe supposedly fixed events or propositions which frequentists disallow. the probability for these events reflects one`s state of knowledge about the event, rather than being an assertion that the unknown event can vary. for example, a bayesian would have no qualms about making statements about the probability that a given die, rolled and hidden from his sight is, for example, a six. a frequentist would be unable to make such a statement, preferring to talk about his confidence in the method when applied to a hypothetically large number of repeated experiments. in the end, they would act in similar ways. when the long run data are available, bayesians and frequentists end up with the same estimates. see also: bayes theorem, kolmogorov`s axioms.
- Вероятность. математическое измерение возможности появления неко-его события, выраженное в виде дроби или процента [30]. значения статистической вероятности лежат в пределах от 1 или 100 процентов (всегда) до 0 или 0 процентов (никогда) [20]. наибольшее приближение к истинной вероятности дает относитель-ная частота события, полученная на основе большой серии измерений или результа-тов [33]. вероятность может быть также определена как выражение в некоторой неопределимой форме "степени уверенности" или как предельная частота события в бесконечной случайной последовательности [49].
- The likelihood of something happening. for example, sale being made.
- Вероятность. математическое измерение возможности появления некоего события, выраженное в виде дроби или процента [30]. значения статистической вероятности лежат в пределах от 1 или 100 процентов (всегда) до 0 или 0 процентов (никогда) [20]. наибольшее приближение к истинной вероятности дает относительная частота события, полученная на основе большой серии измерений или результатов [33]. вероятность может быть также определена как выражение в некоторой неопределимой форме "степени уверенности" или как предельная частота события в бесконечной случайной последовательности [49].
- The relative likelihood of a particular outcome among all possible outcomes.
- Likelihood that an event may occur, expressed as a number between 0 and 1.
Probability algorithm, английский
Вероятностный алгоритм probability-analysys compaction уплотнение (данных) на основе вероятностного анализа
Probability analysis, английский
Systematic procedure for describing and/or calculating the probability of a future event.
Probability and impact matrix, английский
A common way to determine whether a risk is considered low, moderate, or high by combining the two dimensions of a risk, its probability of occurrence, and its impact on objectives if it occurs.
Probability assessment, английский
The process of obtaining probabilities to represent a degree of uncertainty or of belief is referred to as probability assessment. if there are physical models or data, they can be used to estimate the values in a models. often, however, the probabilities need to be specified by an individual or group. there are a wide variety of techniques for evoking these probabilities, using some form of imagination of possible data, analogous reasoning, or estimation of "fair" betting odds. these can lead to sets of distributions for the probabilities and, hence, to quasi-bayesian models see also: bayesian network, quasi-bayesian theory.
Probability based disclosures (approximate or exact), английский
Sometimes although a fact is not disclosed with certainty, the published data can be used to make a statement that has a high probability of being correct.
Experiment, английский
- What distinguishes an experiment from an observational study is that in an experiment, the experimenter decides who receives the treatment.
- Эксперимент
- A scientific test conducted under set conditions the scientists did some experiments to try the new drug on a small sample of people.
- N экспе- римент (см. тж. test) associative ~ псхлнгв. ассоциативный экспе- римент psycholinguistic ~ психолингвистический экс- перимент
- Эксперимент; опыт, опытное исследование
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Type i and type ii errors, английский
- These refer to hypothesis testing. a type i error occurs when the null hypothesis is rejected erroneously when it is in fact true. a type ii error occurs if the null hypothesis is not rejected when it is in fact false. see also significance level and power.
- Ошибки первого рода и ошибки второго рода. см. error (ошибка).
Density, density scale, английский
The vertical axis of a histogram has units of percent per unit of the horizontal axis. this is called a density scale; it measures how "dense" the observations are in each bin. see also probability density.
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