hw3 - Computer Science 340 Reasoning about Computation...

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

View Full Document Right Arrow Icon
Computer Science 340 Reasoning about Computation Homework 3 Due at the beginning of class on Wednesday, October 10, 2007 Problem 1 Suppose you toss three fair, mutually independent coins. Define the following events: A - the event that the first coin is heads B - the event that the second is heads C - the event that the third coin is heads D - the event that the number of heads is even Determine the maximum value of k such that these events are k -wise independent. Problem 2 Let X be a random variable taking integral nonnegative values, Let E [ X ] be its expec- tation, and let E [ X 2 ] denote the expectation of its square. Prove that Pr( X > 0) E [ X ] 2 E [ X 2 ] Hint: You may find the Cauchy–Schwarz inequality useful, which asserts: X i a i b i ± X i a 2 i ! 1 / 2 ± X i b 2 i ! 1 / 2 . If you use the Cauchy–Schwarz inequality, specify what values of a i and b i are. Problem 3
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.

This note was uploaded on 01/29/2008 for the course COS 340 taught by Professor Charikarandchazelle during the Fall '07 term at Princeton.

Page1 / 2

hw3 - Computer Science 340 Reasoning about Computation...

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