Median - Jensen's Inequality For Medians

Jensen's Inequality For Medians

Jensen's inequality states that for any random variable x with a finite expectation E(X) and for any convex function f then

It has been shown that if x is a real variable with a unique median m and f is a C function then

A C function is a real valued function, defined on the set of real numbers R, with the property that for any real t

is a closed interval, a singleton or an empty set.