Question: 3.7. (Sec. 3.2) In variance of the sample correlation coefficient. Prove that r 12 is an invariant characteristic of the sufficient statistics i and S

3.7. (Sec. 3.2) In variance of the sample correlation coefficient. Prove that r 12 is an invariant characteristic of the sufficient statistics i and S of a bivariate sample under location and scale transformations (Xfa = bix;a + Ci' bi> 0, i = 1,2, a =

1, ... , N) and that every function of i and S that is invariant is a function of r 12• [Hint: See Theorem 2.3.2.]

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