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2.2.3 Expectation Value, Variance, Functions of r.v.'s     continued...

We also define ``central'' moments that express the variation of a r.v. about its mean, hence ``corrected for the mean'':

The first central moment is zero. The second central moment is the variance:

It is straightforward to show the following important identity:

We will also find useful the square root of the variance, which is the standard deviation,