Jensens Inequality

Imagine a bunch of datapoints lying on log(y)

Imagine a point (E[y], E[log[y]])

This is the midpoint of all the datapoints This will lie under the log(y) curve by concavity: f((1-a)x + ay) >= (1-a)f(x) + af(y)

The midpoint will lie under the log curve It is thus lower than

(E[y], log(E[y])) which is on the curve.

To Do: Prove Jensen’s Inequality Last Reviewed: 1/19/25