21 Let Y be a Poisson random variable with mean Demonstrate that Pr(Y k) is increasing in for k fixed (Hint If 1 2, then construct coupled Poisson random variables Y1 and Y2 with means 1 and 2 such that Y1 Y2 ) ...

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=+21. Let Y be a Poisson random variable with mean . Demonstrate that Pr(Y k) is

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=+21. Let Y be a Poisson random variable with mean λ. Demonstrate that Pr(Y ≥ k) is increasing in λ for k fixed. (Hint: If λ1 < λ2, then construct coupled Poisson random variables Y1 and Y2 with means

λ1 and λ2 such that Y1 ≤ Y2.)

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Applied Probability

ISBN: 9781441971647

2nd Edition

Authors: Kenneth Lange

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=+21. Let Y be a Poisson random variable with mean . Demonstrate that Pr(Y k) is

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Applied Probability

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