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
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. The function f ( x ) = 2 x, 0 < x < 1 is a PDF. Suppose X is a random variable having this PDF. (a) Calculate E ( X ). (b) Calculate E ( X 2 ). (c) Calculate var( X ). 6-2. The function f ( x,y ) = x + y, 0 < x < 1 , 0 < y < 1 is a PDF. Suppose ( X,Y ) is a random vector having this PDF. (a) Calculate E ( X ). (b) Calculate var( X ). (c) Calculate cov( X,Y ). (By symmetry, E ( Y ) = E ( X ) and var( Y ) = var( X ) so we do not need to calculate them.) 6-3. 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)
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.

This note was uploaded on 02/07/2012 for the course STAT 5101 taught by Professor Staff during the Fall '02 term at Minnesota.

Page1 / 3

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