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symmetric probability distribution : ウィキペディア英語版
symmetric probability distribution

In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function or probability mass function is reflected around a vertical line at some value of the random variable represented by the distribution. This vertical line is the line of symmetry of the distribution. Thus the probability of being any given distance on one side of the value about which symmetry occurs is the same as the probability of being the same distance on the other side of that value.
==Formal definition==

A probability distribution is said to be symmetric if and only if there exists a value x_0 such that
: f(x_0-\delta) = f(x_0+\delta) for all real numbers \delta ,
where ''f'' is the probability density function if the distribution is continuous or the probability mass function if the distribution is discrete.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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