# 10_06_2ans - STAT 400 4.1(continued 1 Fall 2011 Examples...

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

Examples for 10/06/2011 (2) Fall 2011 4.1 (continued) 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? P ( X = 1 Y = 1 ) = p ( 1, 1 ) = 0.10 = 0.25 × 0.40 = P ( X = 1 ) × P ( Y = 1 ). {X = 1} and {Y = 1} are 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)

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 / 4

10_06_2ans - STAT 400 4.1(continued 1 Fall 2011 Examples...

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

View Full Document
Ask a homework question - tutors are online