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# HWK1 - IEOR 4701 Assignment 1 Summer 2011 1 Ross 4.28 A...

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IEOR 4701 Assignment 1 Summer 2011 1. Ross, 4.28 A sample of 3 items is selected at random from a box containing 20 items of which 4 are defective. Find the expected number of defective items in the sample. 2. Ross, 4.41 A man claims to have extrasensory perception. As a test, a fair coin is ﬂipped 10 times, and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP? 3. Ross, Theoretical 4.28. Let X be a negative binomial random variable with parameters r and p , and let Y be a binomial random variable with parameters n and p . Show that P { X > n } = P { Y < r } by means of probabilistic interpretation of these random variables. Do not attempt to give any analytical proof of the preceding. 4. At 8:59 AM, A, B, C are waiting (in that order) outside a bank that will open at 9 AM. The bank has two tellers; each of the requirements that A, B, and C are bringing to the bank are i.i.d. exponentially distributed random variables with mean 1. What is the probability that A is the last one to leave the bank? 5. Ross, Theoretical 4.20

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HWK1 - IEOR 4701 Assignment 1 Summer 2011 1 Ross 4.28 A...

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