Jensen’s Inequality
- relates the value of a convex function of an integral to the integral of the convex function
Statement
Given a convex function 𝑓 and a random variable 𝑋, then:
- 𝑓(𝐄[𝑋]) ≤ 𝐄[𝑓(𝑋)]
as the number of samples of 𝑋 approaches infinity
Visualization
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When 𝑓 is a Straight Line |
When 𝑓 is a Convex Function |
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