Question: For this problem you may require the Schwarz inequality. Given any two rv X and Y with finite variances, the Schwarz inequality states that

For this problem you may require the Schwarz inequality. Given any two

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)] [E(X)E(Y)]. < For a rv Z which is positive, i.e. Z 0, show that P(Z > a) > (E(Z) - a) E(Z) where a > 0 is any arbitrary constant. (Hint: think of a rv which converts into a probability upon taking expectations.)

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