Chapter 5a

# Chapter 5a - Chapter 5 Joint Densities Discrete Variables...

This preview shows pages 1–4. Sign up to view the full content.

Chapter 5 Joint Densities Discrete Variables Let X and Y be random variables. The ordered pair (X,Y) is called a two-dimensional discrete random variable. A function f XY such that f XY (x,y) = P( X=x and Y=y) is called the joint density for (X,Y). Conditions for a Discrete Joint Density 1) f XY (x,y) > 0 2) XY f (x,y) = 1 X Y ∑∑ Example: Show this is a valid joint density function. Y=1 Y=2 X=1 .1 .3 X=2 .4 .2

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

View Full Document
Discrete Marginal Density Let (X,Y) be a two-dimensional discrete random variable with joint density f XY . The marginal density for X, denoted by f X is given by ( ) ( , ) x XY Y f x f x y = The marginal density for Y, denoted by f y , is given by ( ) ( , ) y XY X f y f x y = Expectation of Discrete Joint Densities [ ] ( , ) XY X Y E X xf x y = ∑∑ ∑∑ = X Y y x f x x E ) , ( ) ( 2 2 σ x 2 = E(x 2 ) – [E(x)] 2 [ ] ( , ) XY X Y E Y yf x y = ∑∑ ∑∑ = X Y y x f y y E ) , ( ) ( 2 2 σ Y 2 = E(y 2 ) – [E(y)] 2
(a) Find the marginal density for X. (b) Find the mean and standard deviation for X.

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.

## This note was uploaded on 01/17/2011 for the course STAT 4714 at Virginia Tech.

### Page1 / 13

Chapter 5a - Chapter 5 Joint Densities Discrete Variables...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online