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Homework_1 - ECE600 Random Variables and Waveforms Spring...

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E C E600 Random Variables and Waveforms Prof. Mark R. Bell Spring 20 1 1 MSEE 336 Homework Assignment #1 Should be completed by Session 3 Reading Assignment: Sections 1-1, 1-2, 1-3, 2-1, and 2-2 of Papoulis. 1. Reduce the following expressions to the simplest possible forms: (a) ( A B ) ( B A ). (b) ( A B ) ( A B ). Use DeMorgan’s laws to show that: (c) A ( B C )=( A B ) ( A C ). (d) A B C = A B C . 2. Let { A 1 ,...,A n } be a partition of the space S , and define the family of sets { B 1 ,...,B n } by B j = G A j ,j =1 ,...,n, where G ⊂S . Show that { B 1 n } is a partition of the set G . 3. Let F r =[0 , 1 /r ), r (0 , 1]. Find ± r (0 , 1] F r and ² r (0 , 1] F r . 4. Prove that a finite set with n elements has 2 n distinct subsets. 5. Using the definitions of union, intersection, and complement, show that
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