This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Review: Marginal and Conditional Distributions and Covariance for Continuous Distributions Many topics in the text begin with general case examples and then call attention to families of distribution, especially the normal family. The following uses a polynomial density for two random variables, X and Y, to illustrate finding marginal and conditional distributions for the two variables. Examples below show finding expected values and variances for both marginal distributions. The same approach works for conditional distributions and is not illustrated. The covariance and correlation are concepts introduced in Chapter 5 as is relevance calculation for E(XY) shown in 6. (Some steps are omitted) A bivariate continuous distribution 3 /10 0
1 0
2 , 4
0 1. Find the marginal distribution ,
,  . . for 0 1 .8 .8
5 .8 .8
2  1
0 .56 .8 .8
6 .8 .8
3  1
0 .4 .4 . 56 .0864 2. Find the conditional distribution of f(yx). ,  . . 0 2 3. Covariance and Correlation With E(X) = .56 and V(X) = .0864 from above and given E(Y) = 1.4, V(Y) = .2267 and E(XY) = .76, , Find Cov(X,Y). .76 – 1.4 · .56 Find , , . , .
. .171 .304 4. Find the marginal distribution f(y), E(Y) and V(Y).  . . for 0 2 .1
.1 .1
2
.1
3 .3 .3 .3
4
.3 5 2
0
2

0 1.4  2.187 2.187 1.4 . .2267 5. Find the conditional distribution f(xy) ,  0 1 6. Find E(XY) used in 3. above 4 3 10 3 4
10 .08 .15 .04 .0375  2
0 .76 ...
View
Full
Document
This note was uploaded on 12/20/2011 for the course STAT 344 taught by Professor Staff during the Spring '08 term at George Mason.
 Spring '08
 Staff
 Covariance, Variance

Click to edit the document details