are you saying that you have variables X, Y, and Z ... and, X and Y are
uncorrelated and, Z is the sum of X and Y? ... and you want to find the
covariance (or r i assume) between X and Z?
(or between Y and Z ... same difference)
here is a hint
if X and Y are independent, it is like having two columns of data that have
been placed there totally at random ... knowing X helps not knowing Y, or
vice versa.
when you add together two random and INDEPENDENT variables ... that summed
variable, will IT now have any systematic relationship between either of
the parts that go into the sum?
well, we know that X and Y are uncorrelated so, a big value on X is just as
likely to be associated with a big value on Y ... as a middle sized or
small value on Y, right?
but, that does mean that sometimes, X and Y will both be big ... and the
SUM of the two is big ... and sometimes, X and Y will both be small ... and
the sum of the two will be small, right?
thus, if you look at the sum ... WHEN IT IS LARGE IS HAS TO BE BECAUSE X
AND Y WERE BOTH LARGE IN THAT CASE ... and, when the sum values are small,
it has to be because BOTH X and Y were small too
thus, big and small SUMs will be associated with BIG and SMALL Xs and Ys
... accordingly ... ie, X and Z, and Y and Z ... will be correlated
here is a small minitab simulation of this
Plot
C17 - * **
- 2** *
- * 2 ***
60+ ** ** * **
-* 2 * ** 2* **
- ** * ** ** **
- * * 2 * ** * *
- * ** * 3** * * ** *
45+ * * * *** *** * *
- * * ** *2
- * ** * ** *
- ** * * *
- * * *
30+ **
-
- *
-
--+-+-+-+-+-+C16
304050607080
MTB > corr c16 c17
Pearson correlation of C16 and C17 = -0.005
P-Value = 0.959
then i did the sum of both ... and got the plots of EACH with the sum
MTB > plot c30 c16
Plot
-
C30 - *
-
- * * *
125+* *
-2* *
-*** * * 2*
- *2**
- * 2**2 2 ** ** ** *
100+ * * 3 * 2 * ***
- **3* *22 * *
-* * * ** ** * * *
- ** * ** 2 * *
- ** * * *
75+ *
- 2
- *
--+-+-+-+-+-+C16
304050607080
MTB > plot c30 c17
Plot
-
C30 - *
-
-* * *
125+ **
- * *2
- * * * 2 * **
-*2 2*** *
- *** * *2 * 3 2 2 *
100+ ** * *2 2* * * *
- * * *2 *23* *
-* ** *2* *** ****
-* ** * ** * **
-** * * *
75+ *
- * *
-*
--+-+-+-+-+-+C17
203040506070
At 03:50 AM 1/31/02 -0800, John Smith wrote:
>If I have 3 variables defined as follows:
>
>A, B as independent, uncorrelated values of 0 or 1
>C defined as the logical AND of A&B, such that C=1 if and only if both
>A & B =1, and 0 otherwise.
>
>Example
>
>A=1, B=0 then C=0
>A=0, B=1 then C=0
>A=0, B=1 then C=0
>A=1, B=1 then C=1
>
>My question is, what is the covariance (or how does one begin to
>calculate it) between A and C ?
>
>
>=
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