I'm using a uniform random variable (0 mean, 1 variance) to generate white noise. Then I'm doing a moving average on those samples. I'm trying to figure out the variance of this output distribution.
Since I have a fixed number of independently distributed samples, $n$, that are being added together, this feels like the distribution you get from adding die rolls. Unlike a multinomial distrubution, the trial outcomes get added together and are continuous but bounded. (Well, given that it's floating point data, they're actually discrete but large.)
Does this distribution have a name? From a histogram, it looks like a binomial distribution. Using the variance for a multinomial distribution doesn't really work because I'm adding the samples, not treating them as un-addable categories.