School of Business, Hubei University; School of Economics and Management, Wuhan University

The dependence on the sum of bivariate random vectors with
Farlie-Gumbel-Morgenstern copulas is studied in the paper. Firstly, the Kendall's
 and the Spearman's  on two independent random vectors' sum with the
copulas are deduced, and the specific equation with exponential marginal distribution
is shown. Then, the proposition is proved that there exists no tail-dependence under
some conditions on marginal distribution. Finally, we calculate some numerical
instances for different marginal distributions by using Monte Carlo method. The
conclusions and methods in this paper have theoretical significance for the dependence
between two random indices of the combination of enterprise, and lay foundations for
the further study.