Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 201 / 2 / a

Solution

For an integrable real random variable

X

ψ (θ) = lo g E [e^{θX}], θ \in R,

where

ψ (θ) = + \infty

ψ^{*} (x) = sup_{θ \in R} {θ x - ψ (θ)} .

Solved by gpt-5.6-sol high.

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