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Homework1 - EE 351K Probability Statistics and Random...

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EE 351K Probability, Statistics, and Random Processes SPRING 2012 Instructor:S.Shakkottai [email protected] Homework 1 Problem 1 We are given that P ( A ) = 0 . 6 , P ( B c ) = 0 . 45 , and P ( A B ) = 0 . 85 . Determine P ( B ) and P ( A B ) . Problem 2 Let A and B be two sets. (a) Show that ( A c B c ) c = A B and ( A c B c ) c = A B . (b) Consider rolling a six-sided die once. Let A be the set of outcomes where an odd number comes up. Let B be the set of outcomes where a 1 or a 2 comes up. Calculate the sets on both sides of the equalities in part (a), and verify that the equalities hold. Problem 3 Alice and Bob each choose at random a number between zero and two. We assume a uniform probability law under which the probability of an event is proportional to its area. Consider the following events: A: The magnitude of the difference of the two numbers is greater than 1 / 3 . B: At least one of the numbers is greater than
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