Unformatted text preview: X be the sum of numbers on the two dice. 1. What is E [ X  X 1 is even]? 2. What is E [ X  X 1 = X 2 ]? 3. What is E [ X 1  X = 9]? 4. What is E [ X 1X 2  X = k ] for k in the range [2 , 12]? Problem 6. • For two probabilistic events A and B , does A ∩ B = ∅ imply independence of A and B ? • Give an example where Chernov bounds only give the trivial answer, that is, the obviously correct but not terribly useful p ( X ≥ (1 + ± ) E [ X ]) ≤ 1. • Suppose that n balls are tossed into n bins, where each toss is independent and the ball is equally likely to end up in any bin. What is the expected number of empty bins? What is the expected number of bins with exactly one ball? 1...
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 Fall '11
 Dr.
 Probability theory, Dice, Hypercubes

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