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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

Jensen's inequality is also valid when applied to a sequence of positive numbers. Given numbers

and nonnegative weights

such that

as well as a convex function f, we have that

For a concave function f, we have the opposite inequality sign.

Jensen's inequality serves as logo for the mathematics department of Copenhagen University.