“Probability”的概念、定义、习题解题方法及翻译-数学辞典

单词

Probability

释义

Probability

Probability is the branch of mathematics which studies the possible outcomes of given events together with their relativelikelihoods and distributions. In common usage, the word ``probability'' is used to mean the chance that a particular event(or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as aPercentage between 0 and 100%. The analysis of events governed by probability is called Statistics.

There are several competing interpretations of the actual ``meaning'' of probabilities. Frequentists view probability simplyas a measure of the frequency of outcomes (the more conventional interpretation), while Bayesianstreat probability more subjectively as a statistical procedure which endeavors to estimate parameters of an underlyingdistribution based on the observed distribution.

A properly normalized function which assigns a probability ``density'' to each possible outcome within some interval is calleda Probability Function, and its cumulative value (integral for a continuous distribution or sum for a discrete distribution) is called a Distribution Function.

Probabilities are defined to obey certain assumptions, called the Probability Axioms. Let a Sample Space containthe Union () of all possible events , so

(1)

and let

and

denote subsets of

. Further, let

be the complement of

, so that

(2)

Then the set

can be written as

(3)

where

denotes the intersection. Then





			(4)

where

is the Empty Set.

Let denote the Conditional Probability of given that has already occurred, then

			(5)
			(6)
			(7)
			(8)
			(9)
			(10)

A very important result states that

(11)

which can be generalized to



	(12)

See also Bayes' Formula, Conditional Probability, Distribution, Distribution Function, Likelihood,Probability Axioms, Probability Function, Probability Inequality, Statistics

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