I need a bit of clarification here. In the list of length 100, each entry in that list is a binomial random variable X~Binom(10, .5). The variance of each of

I need a bit of clarification here. In the list of length 100, each entry in that list is a binomial random variable X~Binom(10, .5). The variance of each of these binomials is Var(X) = 10(.5)(.5) = 2.5. But I don't think that's the variance you're talking about. Do you mean the sample variance of the list of length 100? I'm sure that we can figure that out too (or at least what it should look like) but I want to confirm that's the variance you are interested in. Off the top of my head, I think this sample variance should have a roughly Chi-Square distribution, since Binom(10, .5) is close to normal (sort of). In the Wikipedia article, it explains how Chi-Square can be expressed a sum of normals squared (https://en.wikipedia.org/wiki/Chi-squared_distribution https://en.wikipedia.org/wiki/Chi-squared_distribution). I could maybe figure out the actual distribution if you really need it. Then you ask what should the distribution look like? Is this answered by the answer above, or did you mean something related to the 50 samples in particular?