Question: Consider a r.v. X such that P(X > x) = x 1 for x 1. (This is a particular case of the Pareto distribution.)

Consider a r.v. X such that P(X > x) = x⁻¹ for x ≥ 1. (This is a particular case of the Pareto distribution.) Does X have a finite expected value? Does X have a finite certainty equivalent for u(x) = √x? If so, find it.

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