practice1 - CS648 Randomized Algorithms Semester II 2007-08...

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CS648 Randomized Algorithms Semester II, 2007-08 Practice problem sheet Note : More and more problems will be added to this sheet every week. Please attempt these problems on your own. This will help you internalise the techniques of this course. 1. Let X be the random variable for the number of coupons needed to be drawn to collect all n different types of a coupon in the coupon collector’s problem . What is variance of X ? Apply Chebyshev’s inequality to get a bound on Pr [ X > 2 E [ X ]] . 2. Memoryless Guessing To amaze your friends, you have them shuffle a deck of n cards and then turn over one card at a time. Before each card is turned over, you predict its identity. Unfortunately, you don’t have any particular psychic abilities - and you are not good at remembering what has been turned over already- so your strategy is simply to guess a card uniformly at random from the deck. What is the expected number of correct predictions that you would make with this strategy ? 3.
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This note was uploaded on 11/24/2009 for the course CS CS648 taught by Professor Surenderbaswana during the Spring '08 term at University of Massachusetts Boston.

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practice1 - CS648 Randomized Algorithms Semester II 2007-08...

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