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Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
Governments apply probabilistic methods in environmental regulation, entitlement analysis, and financial regulation. An example of the use of probability theory in equity trading is the effect of the perceived probability of any widespread Middle East conflict on oil prices, which have ripple effects in the economy as a whole.
When referring specifically to probabilities, the corresponding term is probabilistic model. All statistical hypothesis tests and all statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference .
Carl Friedrich Gauss made major contributions to probabilistic methods leading to statistics. The mathematical foundations of statistics developed from discussions concerning games of chance among mathematicians such as Gerolamo Cardano, Blaise Pascal, Pierre de Fermat, and Christiaan Huygens.
Historically, attempts to quantify probabilistic reasoning date back to antiquity. There was a particularly strong interest starting in the 12th century, with the work of the Scholastics, with the invention of the half-proof (so that two half-proofs are sufficient to prove guilt), the elucidation of moral certainty (sufficient certainty to act upon, but short of absolute certainty), the ...
In the years to follow, Ludwig Boltzmann translated these 'alterations of arrangement' into a probabilistic view of order and disorder in gas-phase molecular systems.
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In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment.