09hw10

# 09hw10 - EE 464 Mitra Homework 10 Due Monday 10am Spring...

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

EE 464, Mitra Spring 2009 Homework 10 Due Monday, April 13, 2009, 10am This problem set investigates continues the examination of functions of random variables, as well as statistical relationships between multiple random variables and moments of multiple random variables. 1. Short Problems (a) If X 1 and X 2 are positive, identically distributed random variables with mean 1, show that E max { X 1 , X 2 } ≤ 2 . (b) Let Y = X + N , where X is a Bernoulli random variable with parameter p = 0 . 2 and N is Gaussian with zero mean and unit variance. Assume that X and N are independent. Determine the correlation coefficient ρ XY . Note this is akin to looking at the relationship between the transmitted signal and received signal in a binary communications system with coded data (hence p 6 = 0 . 5 ). 2. We have not done much on discrete random variables in lecture. Let X and Y and be two independent, geometric random variables: P [ X = k ] = p X (1 - p X ) k k = 0 , 1 , · · · P [ Y = k ] = p Y (1 - p Y ) k k = 0 , 1 , · · · (a) Determine the joint probability mass function of Z =

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