# Jensen's Inequality If a function $g(x)$ is a [[Convex Function]] i.e. it's first and second order derrivatives are greater than 0, then we have $ \mathbb{E}[g(x)] \geq g[\mathbb{E}(x)] \quad {\text {iff g is convex }} $ Intuition: The average of many (convex) function evaluations is usually greater than the function evaluation of an average. OR, a line connecting two points of a function will be always be below the function. --- ## References 1. Intuition behind Jensen's inequality https://www.youtube.com/watch?v=HfCb1K4Nr8M