Does it follow from the Cauchy-Schwartz inequality (Proposition 1) that for any r.v.s and with

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Does it follow from the Cauchy-Schwartz inequality (Proposition 1) that for any r.v.’s ξ and η with finite second moments, (E{|ξη|})2 ≤ E{ξ2}E{η2}? Which inequality is stronger: this or (1.2.1)?image

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