A convexity gap by Jensen

MediumRandom Variables Expected Value~4m

A quantity $V$ is uniformly distributed on $[0,2]$ . A claim pays the square $V^2$ . What is the fair value $E[V^2]$ of the claim? (to 4 decimals)

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E[V²] is not (E[V])² - the square is convex (Jensen); integrate v²·½ over [0,2].
The gap E[V²] − (E[V])² is exactly Var(V) = 1/3.

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1.3333 (± 0.0005)

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A convexity gap by Jensen

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