QZ 4-A - Y, f Y ( y ). f Y ( y ) = + 2 3 dx y x = 2 3 6 2 +...

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

View Full Document Right Arrow Icon
STAT 400 Fall 2011 Version A Name ANSWERS . Quiz 4 (10 points) Be sure to show all your work; your partial credit might depend on it. If the answer is a function, its support must be included. No credit will be given without supporting work. 1. Let the joint probability density function for ( X , Y ) be f ( x , y ) = 3 y x + , 0 < x < 2, 0 < y < 1, zero otherwise. a) (4) Find the probability P ( X > Y ). P ( X > Y ) = ∫ ∫ + - 1 0 0 3 1 dy dx y x y = + - 1 0 2 2 3 6 1 dy y y = - 1 0 2 2 1 dy y = 6 1 1 - = 6 5 . OR P ( X > Y ) = ∫ ∫ + 1 0 2 3 dy dx y x y = OR P ( X > Y ) = ∫ ∫ ∫ ∫ + + + 2 1 1 0 1 0 0 3 3 dx dy y x dx dy y x x = b) (3) Find the marginal probability density function of
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Y, f Y ( y ). f Y ( y ) = + 2 3 dx y x = 2 3 6 2 + y x x = 3 2 2 y + , 0 &lt; y &lt; 1. 1. (continued) f ( x , y ) = 3 y x + , 0 &lt; x &lt; 2, 0 &lt; y &lt; 1, zero otherwise. c) (3) Are X and Y independent? Justify your answer. No credit will be given without proper justification. Circle one: Yes. No. f X ( x ) = + 1 3 dy y x = 1 6 3 2 + y y x = 6 1 2 + x , 0 &lt; x &lt; 2. f ( x , y ) f X ( x ) f Y ( y ). X and Y are NOT independent ....
View Full Document

This note was uploaded on 02/15/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

Page1 / 2

QZ 4-A - Y, f Y ( y ). f Y ( y ) = + 2 3 dx y x = 2 3 6 2 +...

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