Solve Covariance Question: X,Y Means, Variances, Correlation

[ank0006]

Homework Statement

Let the random variables X and Y have the joint p.m.f.:

f(x,y) = (x+y)/32 x=1,2, y=1,2,3,4.

find the means [tex]\mu[/tex]_x and [tex]\mu[/tex]_y, the variances [tex]\sigma[/tex]²_x and [tex]\sigma[/tex]²_y, and the correlation coefficient [tex]\rho[/tex].

Homework Equations

[tex]\rho[/tex]=(COV(X,Y))/[tex]\sigma[/tex]_x[tex]\sigma[/tex]_y

The Attempt at a Solution

I was able to find both [tex]\mu[/tex]'s:
[tex]\mu[/tex]x= (25/16)
[tex]\mu[/tex]y= (45/16)

and both variances:
[tex]\sigma[/tex]_x=(63/256)
[tex]\sigma[/tex]_y=(295/256)

But I can't seem to find how to get the covariance...I tried just using the 1 and 2 values for x and y, but it hasn't worked. I think I'm getting confused because there are more y values than x values. Any help would be much appreciated!

 

[lanedance]

do you knw the formula for covariance?

you will need to calculate 2x4 terms, one for each x & y outcome