Jensen's Inequality

STA256

If $ϕ$ is convex on an open interval $I$ and $X$ is a random variable whose support is contained in $I$ and has finite expectation.
$ϕ [E (X)] \leq E [ϕ (X)]$
For convex functions, $g$ jensens is $g [E (x)] \leq E [g (x)]$