More generally (and in

probability-speak), for

*any* probability measure, any

random variable X taking value in some

interval `I` and any

convex function `f` defined on

`I`,

**E**`f`(X) ≤ `f`(**E**X)

The same also holds if we replace the interval

`I` with

*any* convex region in

**R**^{n}.

See a proof of the Jensen inequality, if you like.