Given a distribution A and subset of that distribution B, if we only have the mean, variance, and size of both A and B, is there a way to find the variance of A - B? If not, are there other ways to save the distribution that allow this kind of calculation?
Edit: Clarification on problem. I am taking on a very large stream of numbers. The main distribution A contains all of these values. However, each value is tagged with an attribute, denoting a separate dataset that it should be added to. Thus A is the union of all of these smaller datasets/partitions (an example would be distribution B described above). Using the update procedure Iteratively Updating a Normal Distribution, is there a way that I can find the variance of distribution A with all the values of distribution B removed without storing the distributions themselves?