Question: 12.1 Convexity. Prove directly that the function w 7! log Z(w) = log( P x2X ew(x)) is convex (Hint: compute its Hessian).

12.1 Convexity. Prove directly that the function w 7! log Z(w) = log(

P x2X ew(x))

is convex (Hint: compute its Hessian).

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