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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online