hw08_sol - Homework 8 November 2 2007 Problem 1 a f U,V u,v...

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: Homework 8 November 2, 2007 Problem 1. a) f U,V ( u,v ) = 1 . 5 = 2 . ( ≤ U ≤ 1 , ≤ V ≤ U ) f V | U ( v | u ) = f V,U ( v,u ) f U ( u ) = 2 2 u = 1 u , ( ≤ U ≤ 1 , ≤ V ≤ U ) E [ V | U ] = R u v 1 u dv = v 2 2 u | u = u 2 f V ( v ) = R 1 v 2 du = 2- 2 v E [ V ] = R 1 v (2- 2 v ) dv = v 2- 2 / 3 v 2 | 1 = 1 / 3 b) f X ( x ) = 1 , ( ≤ X ≤ 1 ) f Y | X ( y | x ) = 1 x , ( ≤ X ≤ 1 , ≤ Y ≤ X ) E [ Y | X ] = R x y 1 x dy = y 2 2 x = x 2 f X,Y ( x,y ) = f Y | X ( y | x ) f X ( x ) = 1 x f Y ( y ) = R 1 y 1 x dy =- lny E [ Y ] = R 1 y (- lny ) dy =- y 2 4 (2 lny- 1) | 1 = 1 4 c) It is because f X ( x ) are di erent in part a) and part b). Therefore, even though the region and the conditional distribution are the same, the marginal distributions of Y are di erent. Problem 2. Let X= the lifetime of the lightbulb. Y=The lament of the lightbulb. Y = 1 if it has a good lament, Y = 0 if it has a bad lament P ( Y = 1) = 0 . 95 , E ( X | Y = 1) = 600 , E ( X | Y = 0) = 50 E [...
View Full Document

This note was uploaded on 11/12/2008 for the course ORIE 360 taught by Professor Ehrlichman during the Fall '07 term at Cornell.

Page1 / 3

hw08_sol - Homework 8 November 2 2007 Problem 1 a f U,V u,v...

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