# Thread: Correlation coeff. of tetrahedron

1. ## Correlation coeff. of tetrahedron

A tetrahedron with 4 sides (1,2,3,4) is tossed two times. X=min of two observations, Y=max of two observations.
I am trying to find the correlation coefficient of X and Y.

I think I am suppose to make a table for sample space for tosses, a table for the values of X and Y for each outcome, and the table for the pmf.

but i am just having trouble trying to start on the first table...

2. Originally Posted by mightydog78
A tetrahedron with 4 sides (1,2,3,4) is tossed two times. X=min of two observations, Y=max of two observations.
I am trying to find the correlation coefficient of X and Y.

I think I am suppose to make a table for sample space for tosses, a table for the values of X and Y for each outcome, and the table for the pmf.

but i am just having trouble trying to start on the first table...
Suppose that the tetrahedra are distinguishable, then the equally likely outcomes of tossing the two are:

(1,1),(1,2),(1,3),(1,4)
(2,1),(2,2),(2,3),(2,4)
(3,1),(3,2),(3,3),(3,4)
(4,1),(4,2),(4,3),(4,4)

Now your actual experiment has outcomes (a,b) where a is the smaller of the two throws and b the larger. So we can list these and calculate their probabilities using the above table of equally likely outcomes of the underlying experiment.

(1,1) 1/16
(1,2) 2/16
(1,3) 2/16
(1,4) 2/16
(2,2) 1/16
(2,3) 2/16
(2,4) 2/16
(3,3) 1/16
(3,4) 2/16
(4,4) 1/16

CB

3. so now i would just need to find the standard deviation of X and Y as well as the covariance, then correlation coeff=Covariance/(stand.dev(X)*stand.dev(Y))

thanks for the help!

4. i noticed on those probabilities you found that you skipped (2,1),(3,1),(4,1),(3,2),(4,2),(4,3)

is that because X=min of the observations and Y=max of two observations?

5. Originally Posted by mightydog78
i noticed on those probabilities you found that you skipped (2,1),(3,1),(4,1),(3,2),(4,2),(4,3)

is that because X=min of the observations and Y=max of two observations?
For the final calculation you will see that I enumerate them as (a,b) where a<=b, so (2,1) et al are not in the set of outrcomes that are possible when labeled this way.

CB

6. the first list is the sample space for the two tosses and I am assuming the second list of data is a table for the values of X and Y correct? which is why some are left blank since X is the max(a,b) and Y is the min(a,b)

just trying to clarify here

7. Originally Posted by mightydog78
the first list is the sample space for the two tosses and I am assuming the second list of data is a table for the values of X and Y correct? which is why some are left blank since X is the max(a,b) and Y is the min(a,b)

just trying to clarify here
What is left blank?

CB

8. i have the table for X vs. Y and found the marginal probabilities of PY and PX
my question now is how do i find the covariance

the equation for covariance that i have is (E(X-uy)(Y-uy)) / ((stand. dev. of x)*(stand. dev. of y))

how do i find the standard deviation of X or Y when there are 4 different columns for each? should I use the marginal probabilities?