Unformatted text preview: An urn contains n balls numbered 1 ,... ,n . We remove k balls at random (without replacement) and add up their numbers. ±ind the expected value of the sum. 4. Problem. We toss a fair coin a number of times and record the result as a sequence of H and T . We say that a run of 3 heads occurs if we get a pattern ...HHH . .. at some point. ±or example, the sequence THHHHTHHH contains 3 runs of 3 heads. Suppose we toss a coin n times. What is the expected number of runs of 3 heads? 5. Problem. Let X be the number of times we toss a fair coin till the ²rst run of 3 heads occurs. ±ind the expectation of X . 1...
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 Winter '12
 AlexanderBarvinok
 Probability, #, probability density function

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