Ok, this might seem like either a really idiotic question or a really profound one. Consider a probability distribution. I'm picturing a normal distribution, is it meaningful to be able to build up a final probability distribution from a set of narrower probability distributions? Ok, that seems like it came out really poorly so i'll say a few of my thoughts. In quantum mechanics we use [tex]\Psi[/tex](r,t) to represent the wave function for very small particles. Then we square this to get |[tex]\Psi(r)|^2[/tex] which is the probability density. This, I believe would then give me a probability distribution. Which in alot of physics examples is just some multiple of a sine wave. Now, it seems to me(being a novice at both probability and physics) that it may be possible to build up a probability distribution of this sort from several smaller probability distributions through simple interference plotting or fourier analysis or the like. However, I can't resolve to myself why this would be a meaningul thing to do. For instance, multiple probability distributions might imply multiple wave functions and hence multiple particles. And multiple particles would interact usually; thus changing the original wave functions and doing something funky. Can anyone comment on this?