David Mitra had a great, simple answer to a similar question of how to determine the variance of the sum of two correlated random variables. What if, however, I have three normally distributed random variables, only two of which are correlated with one another - how do I find the variance? My thinking is that since
Var(A+B) = Var(A)+ Var(B)+ 2Cov(A,B)
works for two correlated variables, maybe you can just throw in a third, uncorrelated variable C getting:
Var(A+B+C) = Var(A) + Var(B) + Var(C) + 2Cov(A,B)
Also, what if I have more variables and more of those variables are correlated? Say I have variables A, B, C, D and E and A, B and C are all correlated to one another. Would this be a possible solution:
Var(A+B+C+D+E) = Var(A) + Var(B) + Var(C) + Var(D) + Var(E) + 2Cov(A,B) + 2Cov(A,C) + 2Cov(B,C)