# 410Hw02 - STAT 410 Fall 2011 Homework#2(due Friday...

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

Fall 2011 Homework #2 (due Friday, September 9, by 3:00 p.m.) 1. Let X and Y have the joint p.d.f. f X Y ( x , y ) = C x 2 y 3 , 0 < x < 1, 0 < y < x , zero elsewhere. a) What must the value of C be so that f X Y ( x , y ) is a valid joint p.d.f.? b) Find P ( X + Y < 1 ). c) Let 0 < a < 1. Find P ( Y < a X ). d) Let 0 < a < 1. Find P ( X Y < a ). 2. Let X and Y have the joint p.d.f. f X Y ( x , y ) = 20 x 2 y 3 , 0 < x < 1, 0 < y < x , zero elsewhere. a) Find f X ( x ). b) Find E ( X ). c) Find f Y ( y ). d) Find E ( Y ). e) Find Cov ( X, Y ). 3. Suppose the joint probability density function of ( X , Y ) is ( ) = otherwise 0 1 0 , 2 x y y x C y x f a) Find the value of C that would make ( ) y x f , a valid probability density function. b) Find P ( X > 2 Y ) . c) Find P ( X + Y < 1 ). d) Find the marginal densities of X and Y. Are X and Y independent? e)

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.

{[ snackBarMessage ]}

### Page1 / 3

410Hw02 - STAT 410 Fall 2011 Homework#2(due Friday...

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

View Full Document
Ask a homework question - tutors are online