Variance of the sum of multiple random number generators Let's assume I have "n" random number generators, each one has a different variance value, but has the same mean value, zero.
If I generate "n" random numbers with these generators, and sum all of them for an output in an iteration, after many iteration steps, I will get an array as a result. What will be the variance of this output? What is the logic?
For example; 4 random number generators which of variance values are "16","25","36","49". What is the total variance if I sum all of them?


Your $n$ random number generators are like $n$ random variables. The variance of a sum of random variables $X$ and $Y$ is
$$
\operatorname{Var}(X+Y) = \operatorname{Var}(X) + \operatorname{Var}(Y) + 2 \operatorname{Cov}(X, Y)
$$
Assuming that the variables are independent, the covariance is zero, so it reduces to the sum of variances.
