Statistics Solutions

[Solution] Prove that for any X , Y real or complex, | E(XY) |^2≤ E(|X|^2)E(|Y|^2) √E(|X+Y|^2)≤

Question: Prove that for any X , Y real or complex,

  1. \({{\left| E\left( XY \right) \right|}^{2}}\le E\left( |X{{|}^{2}} \right)E\left( |Y{{|}^{2}} \right)\)
  2. \(\sqrt{E\left( |X+Y{{|}^{2}} \right)}\le \sqrt{E\left( |X{{|}^{2}} \right)}+\sqrt{E\left( |Y{{|}^{2}} \right)}\)

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