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cse21_sP07_practice_final

# cse21_sP07_practice_final - CSE 21 Practice Final June 3...

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CSE 21 Practice Final June 3, 2007 There are 15 problems here. (The Final will only have 10 problems and will be a CLOSED BOOK test. However, you may have two 8 1 / 2 by 11 inch sheets of paper with hand-written notes on them, 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! Note : In the final, show your work (especially on the multiple choice problems) if you want to be eligible for partial credit!. 1

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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

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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_sP07_practice_final - CSE 21 Practice Final June 3...

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