I have an experiment in which I want to extract the distribution function of a process. I expect it to be Gaussian. Each data point measured is an entire distribution, f(x), but I am forced to average over many points such that the result of the experiment is the sum of many measurements of f(x). If A and σ are believed to be constants but the mean, μ, varies a little for each point, the resulting sum of distributions appears broader as if σ is larger. My question: If I believe I know the deviation of the mean μ, can this affect be subtracted out so that I am left with the actual value of σ?