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: MathematicsAndStatistics : ProbabilityAxioms -- FrequencyProbability -- PersonalProbability -- EclecticProbability : NormalDistribution -- BinomialDistribution -- PoissonDistribution? |
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: back to MathematicsAndStatistics : ProbabilityAxioms -- ProbabilityTheory -- ProbabilityApplications -- ProbabilityDistributions : StatisticalTheory -- AppliedStatistics? |
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Probability is the mathematical theory we use to describe and quantify uncertainty. Uncertainty can be due to our ignorance, deliberate mixing or shuffling, or due to the essential randomness of Nature. The simplest form of the theory begins with a universe, a finite set of elementary events. We define a weighting function which maps each elementary event into a non-negative number called the weight of the elementary event. We can represent any event by a subset of the universe. The probability of the event is the sum of the weights for all the elementary events in the subset divided by the sum of the weights for the whole universe. Calculation of probabilities can often be determined using CombinaTorics or by applying the definition above directly. |
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Probability is the mathematical theory we use to describe and quantify uncertainty. Uncertainty can be due to our ignorance, deliberate mixing or shuffling, or due to the essential randomness of Nature. In any case, we measure the uncertainty of events on a scale from zero (impossible events) to one (certain events or no uncertainty). ProbabilityAxioms form the basis for mathematical ProbabilityTheory. Calculation of probabilities can often be determined using CombinaTorics or by applying the axioms directly. ProbabilityApplications include even more than Statistics, which is usually based on the idea of ProbabilityDistributions. |
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A probability distribution describes a special universe, a set of real numbers (see AnaLysis?) and how probability is distributed among them to determine a random variable. For every random variable, there is a function called the cumulative distribution function which provides the probability that a given value is not exceeded by the random variable. Several probability distributions are so important that they have been given specific names, the NormalDistribution, the BinomialDistribution, the PoissonDistribution? are just three of them. |
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ProbabilityTheory plays a critical role in the development of StatisticalTheory. Statistics is a branch of applied mathematics which includes planning, summarizing, and interpreting uncertain observations. We describe our knowledge (and ignorance) mathematically and attempt to learn more from whatever we can observe. This requires us to #plan our observations to control their variability (PlanningResearch), #summarize a collection of observations to feature their communality by suppressing details (SummarizingStatisticalData), and #reach consensus about what the observations tell us about the world we observe (InterpretingStatisticalData). |
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Statistics is a branch of applied mathematics which includes planning, summarizing, and interpreting uncertain observations. We describe a universe of possible observations and the probabilities we associate with each. This allows us to plan our observations to control their variability, summarize a collection of observations to feature their communality by suppressing details, and reach consensus about what the observations tell us about the world we observe. |
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There are some ScienCes which use statistics so extensively and have specialized terminology that we recognize special disciplines like: #BioStatistics (including MedicalStatistics?) #PsychologicalStatistics? #BusinessStatistics? and EconomicStatistics? #EngineeringStatistics? #SocialStatistics? (for all the social sciences) Valuable resources on the Web |
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[The Probability Web] [Chance Database] |
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Probability is the mathematical theory we use to describe and quantify uncertainty. Uncertainty can be due to our ignorance, deliberate mixing or shuffling, or due to the essential randomness of Nature. In any case, we measure the uncertainty of events on a scale from zero (impossible events) to one (certain events or no uncertainty).
ProbabilityAxioms form the basis for mathematical ProbabilityTheory. Calculation of probabilities can often be determined using CombinaTorics or by applying the axioms directly. ProbabilityApplications include even more than Statistics, which is usually based on the idea of ProbabilityDistributions.
ProbabilityTheory plays a critical role in the development of StatisticalTheory. Statistics is a branch of applied mathematics which includes planning, summarizing, and interpreting uncertain observations. We describe our knowledge (and ignorance) mathematically and attempt to learn more from whatever we can observe. This requires us to
There are some ScienCes which use statistics so extensively and have specialized terminology that we recognize special disciplines like:
[The Probability Web] [Chance Database]
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