h6 - Stat 5101 (Geyer) Fall 2011 Homework Assignment 6 Due...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Stat 5101 (Geyer) Fall 2011 Homework Assignment 6 Due Wednesday, October 26, 2011 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 6-1. Suppose ( X,Y ) is a continuous random vector having PDF f. Say for each of the following definitions of f whether X and Y are independent or not. (a) f ( x,y ) = 4 xy , 0 < x < 1, 0 < y < 1. (b) f ( x,y ) = 8 xy , 0 < x < y < 1. (c) f ( x,y ) = 144( x- 1 / 2) 2 ( y- 1 / 2) 2 , 0 < x < 1, 0 < y < 1. (d) f ( x,y ) = 288( x- 1 / 2) 2 ( y- 1 / 2) 2 , 0 < x < y < 1. 6-2. Suppose X is a continuous random variable having PDF f ( x ) = 1 + x,- 1 x < 1- x, x 1 , otherwise (a) Find E ( X ). (b) Find E ( X 2 ). (c) Find var( X 2 ). Hint: Since the PDF has a case-splitting formula, you must split integrals into pieces E { g ( X ) } = Z- 1 g ( x ) f ( x ) dx + Z 1 g ( x ) f ( x )...
View Full Document

Page1 / 2

h6 - Stat 5101 (Geyer) Fall 2011 Homework Assignment 6 Due...

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