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Let X be a Poisson(2) random variable, and Y an independent N (1, 3) random variable.

(a) Use Markov’s inequality to bound P (X + Y > 10).

(b) Use Chebyshev’s inequality to bound P (X + Y > 10).

Chebyshev’s inequality does not always give a better estimate than Markov’s inequality. Let X be a random variable with E[X] = 2 and Var(X) = 9. Find the values of t where Markov’s inequality gives a better bound for P(X > t) than Chebyshev’s inequality.

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