{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 09_02 - STAT 410 Examples for Fall 2011 2.5 1 Independent...

This preview shows pages 1–3. Sign up to view the full content.

STAT 410 Examples for 09/02/2011 Fall 2011 2.5 Independent Random Variables 1. Consider the following joint probability distribution p ( x , y ) of two random variables X and Y: x \ y 0 1 2 1 0.15 0.10 0 0.25 2 0.25 0.30 0.20 0.75 0.40 0.40 0.20 Recall: A and B are independent if and only if P ( A B ) = P ( A ) P ( B ) . a) Are events { X = 1 } and { Y = 1 } independent? Def Random variables X and Y are independent if and only if discrete p ( x , y ) = p X ( x ) p Y ( y ) for all x , y . continuous f ( x , y ) = f X ( x ) f Y ( y ) for all x , y . F ( x , y ) = P ( X x , Y y ) . f ( x , y ) = 2 F ( x , y ) / x y . Def Random variables X and Y are independent if and only if F ( x , y ) = F X ( x ) F Y ( y ) for all x , y . b) Are random variables X and Y independent?

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

View Full Document
2. Let the joint probability density function for ( X , Y ) be ( ) + = otherwise 0 1 , 1 0 , 1 0 60 , 2 y x y x y x y x f Recall: f X ( x ) = ( ) 2 2 1 30 x x - , 0 < x < 1, f Y ( y ) = ( ) 3 1 20 y y - , 0 < y < 1. Are random variables X and Y independent? 3. Let the joint probability density function for ( X , Y ) be ( ) + = otherwise 0 1 0 , 1 0 , y x y x y x f Are X and Y independent? 4. Let the joint probability density function for ( X , Y ) be ( ) ( )
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

09_02 - STAT 410 Examples for Fall 2011 2.5 1 Independent...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online