09_12ans - STAT 410 Examples for 09/12/2008 Fall 2008...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: STAT 410 Examples for 09/12/2008 Fall 2008 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 0.15 0 2 0.15 0.35 0.20 a) Find P ( X + Y = 2 ). P ( X + Y = 2 ) = p ( 1, 1 ) + p ( 2, 0 ) = 0.15 + 0.15 = 0.30 . b) Find P ( X > Y ). P ( X > Y ) = p ( 1, 0 ) + p ( 2, 0 ) + p ( 2, 1 ) = 0.15 + 0.15 + 0.35 = 0.65 . 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 marginal probability density functions of X and of Y are given by f X ( x ) = ( ) - , dy y x f , f Y ( y ) = ( ) - , dx y x f ....
View Full Document

This note was uploaded on 10/22/2009 for the course STAT 410 taught by Professor Alexeistepanov during the Fall '08 term at University of Illinois at Urbana–Champaign.

Page1 / 6

09_12ans - STAT 410 Examples for 09/12/2008 Fall 2008...

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

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