I have two distributions which represent the sum of smaller distributions.
Say distribution X is made up of distributions a, b and c: $\mu_a$ = 10, $\sigma_a$ = 3; $\mu_b$ = 15, $\sigma_b$ = 5; $\mu_c$ = 20, $\sigma_c$ = 4; so $\mu_X$ = 45 and $\sigma_X$ = $\sqrt{50}$.
Distribution Y is made up of a, d and e: $\mu_a$ = 10, $\sigma_a$ = 3 (this is of course the same as the a above); $\mu_d$ = 18, $\sigma_d$ = 2; $\mu_e$ = 12, $\sigma_e$ = 4; so $\mu_X$ = 40 and $\sigma_X$ = $\sqrt{29}$.
With this information, is there a way that I can find the correlation/covariance between the two distributions? Would it have to do with how much a contributes to X and Y's means and/or variances?