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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Problem Set 3 Due September 29, 2010 1. The hats of n persons are thrown into a box. The persons then pick up their hats at random (i.e., so that every assignment of the hats to the persons is equally likely). What is the probability that (a) every person gets his or her hat back? (b) the first m persons who picked hats get their own hats back? (c) everyone among the first m persons to pick up the hats gets back a hat belonging to one of the last m persons to pick up the hats? Now assume, in addition, that every hat thrown into the box has probability p of getting dirty (independently of what happens to the other hats or who has dropped or picked it up). What is the probability that (d) the first m persons will pick up clean hats? (e) exactly m persons will pick up clean hats?...
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 Fall '10
 Prof.DimitriBertsekas
 Electrical Engineering, Probability, Probability theory, Randomness

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