cse21_FA07_practice_final

cse21_FA07_practice_final - CSE 21 FA07 Practice Final...

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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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cse21_FA07_practice_final - CSE 21 FA07 Practice Final...

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