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?


If they are normally distributed, the variance of the sum is equal to the sum of the variance of the summands. As pointed out in the comments of my answer, this is not true, i.e. normally distributed variables are not required, but independence is. This can be checked by the following program
import numpy as np

mu, n, vars = 0, 1000000, [16, 25, 36, 49]
sums = np.zeros(n)
for var in vars:
    sums += np.random.normal(mu, var ** 0.5, n)
print(f'sum of variances = {sum(vars)}')
print(f'variance of sums = {np.var(sums):.2f}')

which prints something like
sum of variances = 126
variance of sums = 126.22

