(Solution) - Establish the following generalized version of Theorem 2 The Holder -(2025 Original AI-Free Solution)

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Establish the following generalized version of Theorem 2 (The Holder inequality). Namely, show that for any n (( 2) r.v.s X1,...., Xn and any positive numbers r1, ...., rn with n/r1 + ... + 1/rn = 1, it holds that