1. The problem statement, all variables and given/known data I have a free Brownian particle and its coordinate is given as a function of time: And its first moment, or mean, is given as But what kind of probability density was used to calculate this first moment? 2. Relevant equations I know that the first moment is calculated by using probability density <x> = ∫x*W(x)dx from -infinity to +infinity. X itself is dependent on t, so is it W(x) or W(x,t) or W(t)? I'm little lost on this one. 3. The attempt at a solution I did find some kind of density function in regards to Brownian motion But I can't see how this would yield the correct result. And still, must I integrate over x or t?