hw10_418_10

# hw10_418_10 - 15 a Since f x y is a valid pdf then β...

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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 15. a) Since f ( x, y ) is a valid pdf, then β« β-β β« f ( x, y ) = 1. It yields 1 /c = β« β« ( x,y ) β R 1 dxdy . Then c is 1/area of region R. b) f X ( x ) = β« 1- 1 cdy = 1 / 2, if β 1 < = y < = 1, f Y ( y ) = β« 1- 1 cdx = 1 / 2, if β 1 < = x < = 1. Since f ( x, y ) = 1 / 4 = f X ( x ) β f Y ( y ), X and Y are indepen- dent. c) p ( X 2 + Y 2 < = 1) = β« β« x 2 + y 2 < =1 f ( x ) f ( y ) β« β« ( x,y ) β (- 1 , 1) f ( x ) f ( y ) = Ο/ 4. 20. f X ( x ) = β« β xe- ( x + y dy = xe- x . f Y ( y ) = β« β xe- ( x + y dx = e- y . f ( x, y ) = f X ( x ) f Y ( y ), hence X and Y are independent. f X ( x ) = β« 1 2 dy = 2. f Y ( y ) = β« y 2 dx = 2 y . f ( x, y ) ΜΈ = f X ( x ) f Y ( y ), hence X and Y are NOT independent. 29. a) Since X i are both normally distributed, their sum is also normally dis- tributed. X 1 + X 2 βΌ N (4400 , 105800). p ( X 1 + X 2 > 5000) = p ( Z > 1 . 845) = 1 β Ξ¦(1 . 845) = 0 . 0326....
View Full Document

## This note was uploaded on 01/23/2011 for the course STAT 418 at Penn State.

### Page1 / 2

hw10_418_10 - 15 a Since f x y is a valid pdf then β...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online