# Jensen's inequality

In

mathematics,

**Jensen's inequality** relates the value of a convex function of an

integral to the integral of the convex function. Formally, it states that when

*f* is convex and

*y* is a non-negative function of

*x* fulfilling

then

For example,

In

probability theory, Jensen's inequality is often written using expectations. If

*f* is a convex function and

*X* is a random variable, then