Stat 5101, Fall 1999 (Geyer) Final Exam Solutions

# Stat 5101, Fall 1999 (Geyer) Final Exam Solutions - Up:...

This preview shows pages 1–3. Sign up to view the full content.

Up: Stat 5101 Stat 5101 (Geyer) Final Exam Problem 1 The random vector ( X , Y ) is biivariate normal, hence so is the random vector ( U , V ) because it is a linear transformation of ( X , Y ). To show U and V are independent, we only need show they are uncorrelated by Theorem 4 of Chapter 12 in Lindgren. So we check Alternative Solution The hard way to do this is to use the change of variable to find the joint density of U and V and see that it factors. The joint density of X and Y is Solving for X and Y in terms of U and V gives This transformation has derivative and Jacobian Thus the joint density of U and V is

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

View Full Document
and we see that this indeed factors into a function of u times a function of v . Problem 2 (a) The BUP is , which because functions of the conditioning variable behave like constants in conditional expectation is and the last term is zero because X and Z are independent and E ( Z ) = 0. Thus the BUP is g ( X ) = X 2 (b) The BLUP is where Thus we need to know E ( X ), E ( Y ), , and . From the formulas for the exponential distribution Also
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/28/2010 for the course STAT 5101 taught by Professor Staff during the Spring '02 term at Minnesota.

### Page1 / 7

Stat 5101, Fall 1999 (Geyer) Final Exam Solutions - Up:...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online