here is one VERY simple example
the COV is the AVERAGE of the PRODUCTS of the deviations around the means
... of two variables
if the cov is + .. there is a + relationship between X and Y, if it is -,
there is a - relationsip between X and Y
X Y devX devY (devX)(devY)
10 20 1 -2 - 2
9 24 0 2 0
8 22 -1 0 0
the sum of the products of the deviations around the two means is -2 ....
the average is -2 / 3 = -.67 = the covariance
now, some books will divide by n-1 or 2 in this case ... which would = -2/2
= -1 for the covariance
here is the minitab output ... note, mtb and most software packages will
divide by n-1
Y - *
-
-
22.5+
- *
-
-
-
20.0+ *
-
----+---------+---------+---------+---------+---------+--X
8.00 8.40 8.80 9.20 9.60 10.00
MTB > prin c1-c5
Data Display
Row X Y devX devY product
1 10 20 1 -2 -2
2 9 24 0 2 0
3 8 22 -1 0 0
MTB > sum c5
Sum of product
Sum of product = -2.0000
MTB > cova c1 c2
Covariances: X, Y
X Y
X 1.00000
Y -1.00000 4.00000
MTB > NOTE ... THE INTERSECTION OF THE X AND Y OUTPUT ABOVE ... -1 ... IS
THE COVARIANCE IN THIS PROBLEM
by the way, the CORRELATION is
MTB > corr c1 c2
Correlations: X, Y
Pearson correlation of X and Y = -0.500
At 06:06 PM 2/2/02 +0000, Maja wrote:
>Hi everyone,
>
>we just leanred the cov, and I'm trying to apply the formula
>cov(X,Y)=E(XY)-E(X)E(Y) to the following question
>f(x,y)=(0.6)^x(0.4)^1-x(0.3)^y(0.52)^1-y(2)^xy where poss. values for X and
>Y are x=0,1 and y=0,1.
>The prof. never gave us any examples for cov and neither does the text book.
>Now I don't know what values to plug in for X and what values to plug in for
>Y.
>
>Could someone PLEASE explain to me how am I supposed to know what vales to
>plug into the equation???
>
>TNX
>Maja
>
>
>
>
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