Real random variable Symmetric distribution A real random variable π :π ββ is said to have a symmetric distribution about π iff π βπ has the same distribution as π βπ. prob It follows that π is the Expectation if πΌβ‘[π] exists. Properties Every odd central moment and standardized moment of a symmetrically distributed random variable is zero, e.g. the Skewness. tidy | en | SemBr