Probability_and_Statistics

back to [[Mathematics]] -- [[Science]]

: [[Probability Axioms]] -- [[Probability Theory]] -- [[Probability Applications]] -- [[Probability Distributions]]

: [[Statistical Theory]] -- [[Applied Statistics]] -- [[Planning Research]] -- [[Summarizing Statistical Data]] -- [[Interpreting Statistical Data]]

[[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).

[[Probability Axioms]] form the basis for mathematical [[Probability Theory]]. Calculation of probabilities can often be determined using CombinaTorics or by applying the axioms directly. [[Probability Applications]] include even more than [[Statistics]], which is usually based on the idea of [[Probability Distributions]].

[[Probability Theory]] plays a critical role in the development of [[Statistical Theory]]. [[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 ([[Planning Research]]), 
#summarize a collection of observations to feature their communality by suppressing details ([[Summarizing Statistical Data]]), and 
#reach consensus about what the observations tell us about the world we observe ([[Interpreting Statistical Data]]).

There are some [[Science]]s which use [[statistics]] so extensively and have specialized terminology that we recognize special disciplines like:
#BioStatistics
#[[Psychological Statistics]]
#[[Business Statistics]]
#[[Economic Statistics]]
#[[Engineering Statistics]]
#[[Social Statistics]] (for all the ''social'' sciences)
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Some valuable resources on the Web are:
[http://www.clarkson.edu/~dobrowb/probweb/probweb1.html The Probability Web] and 
[http://www.dartmouth.edu/~chance/ Chance Database]
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[[Dick Beldin]]