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Intermediate Proof

Jensen's Inequality for Convex Functions

Students often swap the inequality direction. A helpful mnemonic is that for convex (bowl-shaped) functions, the average of the outputs is always 'heavier' or 'higher' than the output of the average input, hence f(mean)mean(f) f(\text{mean}) \leq \text{mean}(f) .
Institutional Reference: Fundamentals of Optimization
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