Computer Science 174 - Fall 2001 - Steiger - Midterm 1

Computer Science 174 - Fall 2001 - Steiger - Midterm 1 - 1...

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Unformatted text preview: 1 CS174 October 11,2001 TEST 1 Instructions: Do all your work in the blue exam books. Please write your answers IN THE GIVEN ORDER, though you may solve problems in any order. There is no need to reduce answers to simplest terms. You may use one page of prepared notes, but all work must be your own. Show ALL your work. You will get little or no credit for an unexplained answers. The value of each question appears in parentheses. Use this as a guide in allocating your time. There are 70 points, and you have 70 minutes. 1. (20 pts) This question deals with random permutations. The probability space is )} ,..., ( { 1 n S π π π = = of permutations of 1,..., n under equally likely probability. k n 2 = is even. (a) Let A be the event that even and odd values alternate (if i π odd, 1 + i π even; if i π even, 1 + i π odd). Find ) ( A P and explain how you did it. What is the limit of ) ( 2 A P n as ∞ → n ? Explain....
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Computer Science 174 - Fall 2001 - Steiger - Midterm 1 - 1...

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