# hw1 - EE 351K Probability Statistics and Random Processes...

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EE 351K Probability, Statistics, and Random Processes SPRING 2009 Instructor: Shakkottai/Vishwanath { shakkott,sriram } @ece.utexas.edu Homework 1 Due Wednesday, Jan 28 2009 at 5pm Problem 1 We are given that P ( A ) = 0 . 3 , P ( B c ) = 0 . 45 , and P ( A B ) = 0 . 6 . 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 a 3 or 4 comes up. Let B be the set of outcomes where a prime number 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 one. 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 / 2 . B: At least one of the numbers is greater than

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## This note was uploaded on 10/26/2009 for the course EE 351k taught by Professor Bard during the Spring '07 term at University of Texas.

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hw1 - EE 351K Probability Statistics and Random Processes...

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