For this problem you may require the Schwarz inequality. Given any two rv X and Y...

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For this problem you may require the Schwarz inequality. Given any two rv X and Y with finite variances, the Schwarz inequality states that [E(XY)]² ≤ [E(X²)E(Y²)]. < For a rv Z which is positive, i.e. Z≥ 0, show that P(Z > a) > (E(Z) - a)² E(Z²) where a > 0 is any arbitrary constant. (Hint: think of a rv which converts into a probability upon taking expectations.) For this problem you may require the Schwarz inequality. Given any two rv X and Y with finite variances, the Schwarz inequality states that [E(XY)]² ≤ [E(X²)E(Y²)]. < For a rv Z which is positive, i.e. Z≥ 0, show that P(Z > a) > (E(Z) - a)² E(Z²) where a > 0 is any arbitrary constant. (Hint: think of a rv which converts into a probability upon taking expectations.)

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