Assume that x1, x2...xn are independent r.v's find the pf of y=sumition aixi where ai are constants

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X₁, X₂, ...,Xₙ are i.i.d. positive RVs, 𝜃₁≽𝜃₂≽...≽𝜃ₙ≻0 are constants⟹(Σ𝜃ᵢ)⁻¹≼𝔼{Xₙ(Σ𝜃ᵢXᵢ)⁻¹}X₁, X₂, ...,Xₙ are i.i.d. positive RVs, 𝜃₁≽𝜃₂≽...≽𝜃ₙ≻0 are constants⟹(Σ𝜃ᵢ)⁻¹≼𝔼{Xₙ(Σ𝜃ᵢXᵢ)⁻¹}
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