This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full 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. 61. 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. 62. 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 casesplitting 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
 Spring '11
 Staff

Click to edit the document details