In sampling from a bivariate normal distribution, it is true that the sample correlation coefficient R has an approximate normal distribution N[, (1 2)2/n]

In sampling from a bivariate normal distribution, it is true that the sample correlation coefficient R has an approximate normal distribution N[ρ, (1 − ρ2)2/n] if the sample size n is large. Since, for large n, R is close to ρ, use two terms of the Taylor's expansion of u(R) about ρ and determine that function u(R) such that it has a variance which is (essentially) free of p. (The solution of this exercise explains why the transformation (1/2) ln[(1+R)/ (1 − R)] was suggested.)