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Frequency theory of probability
| Glossary of Statistical Terms |
Probability, theories of
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Probability, theories of, английский
A theory of probability is a way of assigning meaning to probability statements such as "the chance that a thumbtack lands point-up is 2/3." that is, a theory of probability connects the mathematics of probability, which is the set of consequences of the axioms of probability, with the real world of observation and experiment. there are several common theories of probability. according to the frequency theory of probability, the probability of an event is the limit of the percentage of times that the event occurs in repeated, independent trials under essentially the same circumstances. according to the subjective theory of probability, a probability is a number that measures how strongly we believe an event will occur. the number is on a scale of 0% to 100%, with 0% indicating that we are completely sure it won`t occur, and 100% indicating that we are completely sure that it will occur. according to the theory of equally likely outcomes, if an experiment has n possible outcomes, and (for example, by symmetry) there is no reason that any of the n possible outcomes should occur preferentially to any of the others, then the chance of each outcome is 100%/n. each of these theories has its limitations, its proponents, and its detractors.
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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.
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Probability, theories of, английский
A theory of probability is a way of assigning meaning to probability statements such as "the chance that a thumbtack lands point-up is 2/3." that is, a theory of probability connects the mathematics of probability, which is the set of consequences of the axioms of probability, with the real world of observation and experiment. there are several common theories of probability. according to the frequency theory of probability, the probability of an event is the limit of the percentage of times that the event occurs in repeated, independent trials under essentially the same circumstances. according to the subjective theory of probability, a probability is a number that measures how strongly we believe an event will occur. the number is on a scale of 0% to 100%, with 0% indicating that we are completely sure it won`t occur, and 100% indicating that we are completely sure that it will occur. according to the theory of equally likely outcomes, if an experiment has n possible outcomes, and (for example, by symmetry) there is no reason that any of the n possible outcomes should occur preferentially to any of the others, then the chance of each outcome is 100%/n. each of these theories has its limitations, its proponents, and its detractors.
Normal curve, английский
The normal curve is the familiar "bell curve:," illustrated on this page. the mathematical expression for the normal curve is y = (2×pi)−½e−x2/2, where pi is the ratio of the circumference of a circle to its diameter (3.14159265…), and e is the base of the natural logarithm (2.71828…). the normal curve is symmetric around the point x=0, and positive for every value of x. the area under the normal curve is unity, and the sd of the normal curve, suitably defined, is also unity. many (but not most) histograms, converted into standard units, approximately follow the normal curve.
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