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 30 40 50 60 70 80 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 30 40 50 60 70 80 MTB > plot c30 c17 Plot - C30 - * - - * * * 125+ * * - * *2 - * * * 2 * ** - * 2 2*** * - * ** * *2 * 3 2 2 * 100+ ** * *2 2* * * * - * * *2 *23* * - * ** *2* *** ** ** - * * * * ** * ** - * * * * * 75+ * - * * - * --+---------+---------+---------+---------+---------+----C17 20 30 40 50 60 70 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 ? > > >================================================================= >Instructions for joining and leaving this list, remarks about the >problem of INAPPROPRIATE MESSAGES, and archives are available at > http://jse.stat.ncsu.edu/ >================================================================= _________________________________________________________ dennis roberts, educational psychology, penn state university 208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED] http://roberts.ed.psu.edu/users/droberts/drober~1.htm ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =================================================================