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title: "The mean"
canonical: "https://modelassist.epixanalytics.com/space/EA/26574925/The%20mean"
format: markdown
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# The mean *m*
The mean, also known as the expected value or average, is given by:
> Macro (inline-media-image)
> Macro (mathinline)
for discrete variables
> Macro (inline-media-image)
> Macro (mathinline)
for continuous variables
The mean is known as *the first moment about zero*. It can be considered to be the center of gravity of the distribution. If one were to cut out the probability density function drawn on a piece of card, the mean is the value at which the distribution would balance.
### ***Example***
The mean of the Uniform(1,3) distribution is calculated as follows:
> Macro (mathblock)
The mean has the following properties:
*m*X+Y = *m*X + *m*Y,
*m*X-Y = *m*X - *m*Y,
*m*X*Y = *m*X**m*Y
where *X* and *Y* are positive, uncorrelated random variables.
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