MIT6_042JF10_final_2008 - 6.042/18.062J Mathematics for...

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6.042/18.062J Mathematics for Computer Science December 17, 2008 Tom Leighton and Marten van Dijk Final Exam Name: • This final is closed book , but you may have three 8.5” × 11” sheets with notes in your own handwriting on both sides. • You may not use a calculator or a Python interpreter, and while exercising skill with a PostScript interpreter would highly impress at least one member of the course staff, you are not allowed to use that either. You may work with any of the follow- ing: a slide rule, an abacus, a Curta, Napier’s bones, any original version of the Antikythera mechanism, an Enigma machine, and/or the difference engine. You are also permitted to use a perpetual motion machine as a source of energy, and an antigravity device to elevate yourself above the rest of the class. • You may assume all of the results presented in class. • Please show your work. Partial credit cannot be given for a wrong answer if your work isn’t shown. • Write your solutions in the space provided. If you need more space, write on the back of the sheet containing the problem. Please keep your entire answer to a prob- lem on that problem’s page. • Be neat and write legibly. You will be graded not only on the correctness of your answers, but also on the clarity with which you express them. • If you get stuck on a problem, move on to others. The problems are not arranged in order of difficulty. • Please resist the urge to roll on the floor laughing out loud. • You have three hours to complete the exam. Problem 1 2 3 4 5 6 7 8 9 10 Total Points 25 25 25 15 15 15 25 15 20 20 200 Score Grader
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Final Exam Problem 1. [25 points] The Final Breakdown Suppose the 6.042 final consists of: • 36 true/false questions worth 1 point each. • 1 induction problem worth 15 points. • 1 giant problem that combines everything from the semester, worth 49 points. Grading goes as follows: • The TAs choose to grade the easy true/false questions. For each individual point, they flip a fair coin. If it comes up heads, the student gets the point. • Marten and Brooke split the task of grading the induction problem. With 1/3 probability, Marten grades the problem. His grading policy is as follows: Either he gets exasperated by the improper use of math symbols and gives 0 points (which happens with 2/5 probability), or he finds the answer satisfactory and gives 15 points (which happens with 3/5 probability). With 2/3 probability, Brooke grades the problem. Her grading policy is as follows: She selects a random integer point value from the range from 0 to 15, inclusive, with uniform probability. • Finally, Tom grades the giant problem. He rolls two fair seven -sided dice (which have values from 1 to 7, inclusive), takes their product, and subtracts it from 49 to determine the score. (Example: Tom rolls a 3 and a 4. The score is then 49 3 4 = · 37.) Assume all random choices during the grading process are mutually independent. The problem parts start on the next page. Show your work to receive partial credit.
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MIT6_042JF10_final_2008 - 6.042/18.062J Mathematics for...

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