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Unformatted text preview: CSE 21 FA07 Practice Final December, 2007 There are 15 problems here. The Final could have fewer problems and will be a CLOSED BOOK test. However, you may bring along two 8 1 / 2 by 11 inch sheets of paper with hand written notes on both sides, if you wish. Also, calculators can be used but shouldn’t be necessary since answers can be left in unexpanded form, i.e., using ! and ( x y ) . Good luck! 1 1. Find general solutions to the following two recurrences: (a) (10 points) g ( n + 2) = 3 g ( n + 1) + g ( n ) , n ≥ 0, where g (0) = 1 , g (1) = 1 . (b) (10 points) h ( n + 2) = 8 h ( n + 1) 16 h ( n ) , n ≥ 0, where h (0) = 1 , h (1) = 1 . 2 2. (10 points) Three light bulbs are chosen at random from a set of twelve light bulbs, five of which are defective. What is the expected number of defective bulbs that are chosen? 3 3. (10 points) If f = (123)(45) , g = (15)(24)(3) and h = (13542) are three permutations in cycle form, which of the following compositions is equal to the permutation (1)(2453)?...
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 Spring '08
 Graham
 Probability theory, 1%

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