final

final - Homework 10 Section 7.1, problems 2, 5, Section...

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

View Full Document Right Arrow Icon
Homework 10 Section 7.1, problems 2, 5, Section 7.2, problems 2, Section 7.3, problems 8. Exercise Problems for Final Exam 1. Suppose that random variables X and Y have joint density function of the form f ( x,y ) = Ce -| x + y |-| x - y | . Determine the value of C , find the marginal density function of X and Y , find E ( X k ) ,V ar ( X ), find E ( XY ) and σ XY = E ( XY ) - E ( X ) E ( Y ), find the conditional density function f Y | X ( y | x ), find the conditional expected value E ( Y | X ), 2. Let X and Y be independent uniformly distributed random variables taking values in the interval [0 , 2]. Find the density functions of Z = X + Y and W = X - Y . Are Z and W independent? What is the covariance σ ZW = E ( ZW ) - E ( Z ) E ( W )? Are they uncorrelated? 3. Let X 1 , ··· ,X n , ··· be an i.i.d. sequence of random variables having 1 - e - λx : x 0 and 0 : x < 0 as their common distribution function. What is the distribution function of
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 / 3

final - Homework 10 Section 7.1, problems 2, 5, Section...

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