Real random variable

Symmetric distribution

A real random variable 𝑋 :𝜉 →ℝ is said to have a symmetric distribution about 𝜇 iff 𝑋 −𝜇 has the same distribution as 𝜇 −𝑋. #m/def/prob It follows that 𝜇 is the Expectation if 𝔼⁡[𝑋] exists.

Properties

• Every odd central moment and standardized moment of a symmetrically distributed random variable is zero, e.g. the Skewness.

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