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Homework_2

# Homework_2 - (b at most one of the events A B C occurs(c...

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ECE600 Random Variables and Waveforms Mark R. Bell Spring 20 1 1 MSEE 336 Homework Assignment #2 Should be completed by Session 6 Reading Assignment: Section 2-3 of Papoulis, and review all of Ch. 2. and class notes. ( n.b., Problem numbers from Papoulis listed below are valid for both the 3rd and 4th editions.) 1. Papoulis, Problem 2-2. 2. Papoulis, Problem 2-3. 3. Papoulis, Problem 2-4. 4. Papoulis, Problem 2-5. 5. Papoulis, Problem 2-6. 6. Papoulis, Problem 2-7. 7. Papoulis, Problem 2-8. 8. Papoulis, Problem 2-9. 9. Show that for any two events A and B in a probability space ( S , F , P ) the following relationship holds: P ( A ) P ( B ) P ( A B ) = P ( A B ) P ( A ) P ( B ) = P ( A B ) P ( A ) P ( B ) . 10. Express each of the following events in terms of the events A , B , and C and the operations of complementation, union, and intersection: (a) at least one of the events A , B , C occurs;
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Unformatted text preview: (b) at most one of the events A , B , C occurs; (c) none of the events A , B , C occurs; (d) aall three events occur; (e) exactly one of the events A , B , C occurs; (f) A and B occur, but not C ; (g) A occurs, if not then B does not occur either. 11. Let S be the sample space corresponding to the random experiment of tossing a coin three times and noting the sequence of H and T ( heads and tails ). Let A be the event that heads occurs exactly twice, let B be the event that at least two heads appear, and let C be the event that heads appears after tails has appeared at least once. (a) Give the elements of A , B , and C ; (b) Describe the events: (i) A ∩ B , (ii) A ∩ B , (iii) A ∩ C . – 1 –...
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