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CS70_sp01_mt1

# CS70_sp01_mt1 - CS 70 Midterm 1 Midterm Exam 1 CS70...

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Midterm Exam 1 CS70 Blum/Wagner, 9 March 2001 This is a CLOSED BOOK examination. One page of notes is permitted. Calculators are permitted. Do all your work on the pages of this examination. Give reasons for all your answers. Problem 1 (Short answer grab-bag) [10 Points] For parts (a)-(c), justify your answer briefly. (a) [2 Points] True or False: (P => Q) => (Q => P) always holds, for all propositions P, Q. (b) [3 Points] True or False: ((P v Q) => Q) => (Q => (P v Q)) always holds, for all propositions P, Q. (c) [3 Points] Recall that two sest S,T are said to be disjoint if = Ø. Can two events A and B be simultaneously independent and disjoint? (d) [2 Points] Recall that two random variables X and Y are independent just if the pair of events X= i and Y= j are independent no matter how you choose the values i and j . Which of the following most accurately expresses the proposition that X and Y are not independent? (You do not need to justify your answer.) Problem 2 (Permutations) [25 Points] Let S be the sample space of all permutations on the n letters {1,2,..., n

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CS70_sp01_mt1 - CS 70 Midterm 1 Midterm Exam 1 CS70...

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