{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

10_06_1 - STAT 400 Examples for(1 Fall 2011 Multivariate...

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

View Full Document Right Arrow Icon
STAT 400 Examples for 10/06/2011 (1) Fall 2011 Multivariate Distributions Let X and Y be two discrete random variables. The joint probability mass function p ( x , y ) is defined for each pair of numbers ( x , y ) by p ( x , y ) = P( X = x and Y = y ). Let A be any set consisting of pairs of ( x , y ) values. Then P ( ( X, Y ) A ) = ( ) ( ) ∑ ∑ y x A y x p , , . Let X and Y be two continuous random variables. Then f ( x , y ) is the joint probability density function for X and Y if for any two-dimensional set A P ( ( X, Y ) A ) = ( ) ∫∫ A dy dx y x f , . 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 2 0.25 0.30 0.20 a) Find P ( X + Y = 2 ). b) Find P ( X > Y ).
Background image of page 1

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

View Full Document Right Arrow Icon
The marginal probability mass functions of X and of Y are given by p X ( x ) = ( ) y y x p all , , p Y ( y ) = ( ) x y x p all , . The
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 4

10_06_1 - STAT 400 Examples for(1 Fall 2011 Multivariate...

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

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online