Editing Mean (section)

====Mean of a probability distribution====
{{Main|Expected value}}
{{See also|Population mean}}
The mean of a [[probability distribution]] is the long-run arithmetic average value of a [[random variable]] having that distribution. If the random variable is denoted by <math>X</math>, then the mean is also known as the [[expected value]] of <math>X</math> (denoted <math>E(X)</math>). For a [[discrete probability distribution]], the mean is given by <math>\textstyle \sum xP(x)</math>, where the sum is taken over all possible values of the random variable and <math>P(x)</math> is the [[probability mass function]]. For a [[continuous probability distribution|continuous distribution]], the mean is <math>\textstyle \int_{-\infty}^{\infty} xf(x)\,dx</math>, where <math>f(x)</math> is the [[probability density function]].<ref name=":1">{{Cite web|last=Weisstein|first=Eric W.|title=Population Mean|url=https://mathworld.wolfram.com/PopulationMean.html|access-date=2020-08-21|website=mathworld.wolfram.com|language=en}}</ref> In all cases, including those in which the distribution is neither discrete nor continuous, the mean is the [[Lebesgue integration|Lebesgue integral]] of the random variable with respect to its [[probability measure]]. The mean need not exist or be finite; for some probability distributions the mean is infinite ({{math|+&infin;}} or {{math|−&infin;}}), while for others the mean is [[Undefined (mathematics)|undefined]].