{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# HW2 - ENEE 620/FALL 2010 RANDOM PROCESSES IN COMMUNICATION...

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

ENEE 620/FALL 2010 RANDOM PROCESSES IN COMMUNICATION AND CONTROL HOMEWORK # 2: Please work out the ten (10) problems stated below – GS refers to the text: Geoffrey R. Grimmett and David R. Stirzaker, Probability and Random Processes , Oxford University Press, Oxford (UK), 2001. With this in mind, Exercise 1.2-2 (GS) refers to Exercise 2 for Section 1.2 of GS while Problem 1-31 (GS) refers to Problem 31 for Chapter 1 in GS. Show work and explain reasoning. Three (3) problems, selected at random amongst these ten problems, will be marked. When not specified, an underlying probability triple (Ω , F , P ) is always assumed. 1. Recall that a collection of events A 1 , . . . , A n is said to be mutually independent if P [ i J A i ] = i J P [ A i ] for any subset J of { 1 , . . . , n } . Now consider a countably infinite collection { A n , n = 1 , 2 , . . . } of events. It is tempting to define the mutual independence of these events through the requirement P [ n J A n ] = n J P [ A n ] for any subset J of { 1 , 2 , . . . } . Explain why this is not a meaningful definition.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern