Postgraduate entrance examination, probability theory. If you toss a coin n times, X and Y represent the times of head-up and head-down respectively, then ρ xy =-

If Xi is determined and Yi=n-Xi is also determined, X and Y should be completely related. x，。 Y stands for the average of x and y, so: Yi? . Y=(n？ Xi)？ (n？ . X)=。 x？ Xi, thus: r = ∑ [(xi? . X) (easy? . Y)][∑(Xi？ . X)2∑ (Easy? . Y)2]=？ ∑[(Xi？ . X)2][∑(Xi？ . X)2∑(Xi？ . X)2]=？ 1, so the correlation coefficient is-1. In fact, cov(X, Y)=cov(X, n-X)=-DX, and DY=D(n-X)=DX. The definition of correlation coefficient is: ρ xy = CoV (x, x). DXDXDY=？ 1, so choose a.