Let A denote the percentage of one constituent in a ran- domly selected rock specimen, and let B denote the per- centage of a second constituent in that same specimen. Suppose D and E are measurement errors in determining the values of A and B so that measured values are X = A + D and Y B+E, respectively. Assume that measurement errors are independent of one another and of actual values.

a. Show that Corr(X, Y) = Corr(A, B) VCorr(X, X) VCorr(Y, Y) where X, and X, are replicate measurements on the value of A, and Y, and Y, are defined analogously with respect to B. What effect does the presence of measure- ment error have on the correlation?

b. What is the maximum value of Corr(X, Y) when Corr(X, X)=.8100 and Corr(Y, Y2) = .9025? Is this disturbing?