##  [Jensen's Inequality](/jensens-inequality) 

  ##  [Jensen's Inequality](https://puremath.quantumdictionary.io/jensens-inequality-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An inequality stating that for a convex function φ and an integrable random variable X (or measurable function) the convex function evaluated at the expectation (or integral average) is at most the expectation of the convex function: φ(E[X]) ≤ E[φ(X]).