In this paper, we provide some exact expressions in a close form for central moment envelope correlation coefficient (ECC) and joint moment ECC of the maximal ratio combining (MRC) output in correlated Rayleigh and Rician fading environments. Besides, we deduce an analytical formula for average capacity with minor approximation. With these expressions, a simple relationship between joint moment ECC and the average capacity is presented, which means that only joint moment ECC can be used to predict system performance such as average channel capacity quantitatively. Furthermore, it has been demonstrated by Monte Carlo simulation that our analysis are matched with the numerical results excellently.