L12_S10 - AMS 507, Fall Semester, 2010 Chapter Six Jointly...

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

View Full Document Right Arrow Icon
AMS 507, Fall Semester, 2010 Chapter Six Jointly Distributed Random Variables 6.1. Joint Distribution Functions The joint cumulative probability distribution function of any two random variables X and Y is defined by . , }, , { ) , ( , < < - = b a b Y a X P b a F Y X The cumulative distribution function of X is related to the joint cumulative probability distribution function by ), , ( ) ( , = a F a F Y X X and the cumulative distribution function of Y is related to the joint cumulative probability distribution function by ). , ( ) ( , b F b F Y X Y = In this context, ) ( a F X and ) ( b F Y are referred to as the marginal distribution functions of X and Y respectively. The probability of a rectangular region is given by ). , ( ) , ( ) , ( ) , ( } , { 1 1 1 2 , 2 1 , 2 2 , 2 1 2 1 b a F b a F b a F b a F b Y b a X a P Y X Y X Y X + - - = < < Definition of joint probability mass function of two discrete random variables: p x y P X x Y y ( , ) ( , ) . = = = One can calculate the marginal cumulative probability function of X as well as the marginal cumulative probability 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
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

L12_S10 - AMS 507, Fall Semester, 2010 Chapter Six Jointly...

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