{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

slides17

# slides17 - Lecture Stat 302 Introduction to Probability...

This preview shows pages 1–5. Sign up to view the full content.

Lecture Stat 302 Introduction to Probability - Slides 17 AD March 2010 AD () March 2010 1 / 11

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

View Full Document
Jointly Distributed Random Variables Assume we have two r.v. X and Y , then we de°ne the joint c.d.f. F ( a , b ) = P ( X ° a , Y ° b ) The c.d.f of X is F X ( a ) = P ( X ° a , Y ° ) = lim b ! P ( X ° a , Y ° b ) = lim b ! F ( a , b ) Similarly we have that the c.d.f. of Y is F Y ( b ) = P ( X ° , Y ° b ) = lim a ! F ( a , b ) AD () March 2010 2 / 11
Jointly Distributed Random Variables Consider P ( X > a , Y > b ) = 1 ± P ( f X > a , Y > b g c ) = 1 ± P ( f X > a , Y > b g c ) = 1 ± P ( f X > a g c [ f Y > b g c ) = 1 ± P ( f X ° a g [ f Y ° b g ) = 1 ± [ P ( X ° a ) + P ( Y ° b ) ± P ( X ° a , Y ° b )] = 1 ± F X ( a ) ± F X ( b ) + F ( a , b ) . For discrete variables, we work directly with the joint pmf p ( x , y ) = P ( X = x , Y = y ) from which we obtain p X ( x ) = y p ( x , y ) , p Y ( y ) = x p ( x , y ) . AD () March 2010 3 / 11

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

View Full Document
Joint Probability Density Function If both X and Y are jointly continuous, then their joint p.d.f. is a non-negative function f ( x , y ) such that for any set C P f ( X , Y ) 2 C g = Z Z ( x , y ) 2 C f ( x , y ) dxdy .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 11

slides17 - Lecture Stat 302 Introduction to Probability...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online