let's say I have two random variables, both have a mean of 0, one has a variance of 2, the other has a variance of 3. How can you determine the distribution of their sum?
2026-03-26 06:28:22.1774506502
Distribution of sum of two random variables
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All you can say is that the mean of the sum is the sum of the means, i.e. $0$, and that the variance of the sum is between $5-\sqrt{24}$ and $5+\sqrt{24}$ (about 0.1 and 9.9).
If the two random variables are independent or at least uncorrelated then the variance of the sum is the sum of the variances, i.e. $5$.