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Unformatted text preview: ω 1 ∈ A , X ( ω 1 ) = 1 , and X ( ω 2 ) = 2 . For an arbitrary ω ∈ Ω , what possible values can X ( ω ) take? Justify your answer fully. b. Given the information in part a and that P ( A ) = 0 . 2 , ﬁnd the distribution of X (or characterize it in terms of a CDF, PDF, or PMF). 3 4. (10 pts.) Consider a discrete real random variable X , with probability generating function G X . a. Use the Markov inequality to derive an upper bound involving G X , analogous to the Chernoff bound, for the tail probability P { X ≥ a } , a ∈ R . b. Apply part a to obtain a tailprobability bound for the Poisson distribution with parameter λ , assuming a ≥ λ . 4...
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 Spring '08
 Staff
 Probability theory, Probability space, Borel, Chernoff, Ω. Suppose C1

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