3 ms·

"Now it should be fairly clear intuitively that at least roughly increments, that is, arrivals of points, are stationary in time and independent." That's not i

• graycat 12y ago
  Tell you what: I'll give you the history of the solar storms, mass ejections, up-chucks, whatever, and you tell me when the next up-chuck is. If it can't be done, then independence has to hold. If in practice we don't have a clue, then intuitively we have to guess that we have a good first-cut approximation to independence. Here I'm omitting the little derivation in terms of conditional probability -- I've done it too often in the past and am in a hurry this morning. "The same source" doesn't have to mean much. We can flip the same coin and get independent results. The internals of the sun are complicated with, no doubt, a lot of randomness, i.e., roiling and boiling. For a good first cut in practice, at least over time intervals longer than, say, a week, we assume independence. Or, I've got a pot of soup overheated and boiling on the stove, and occasionally it splatters and puts a mess on the stove top. When's the next splatter? Who knows. So, first-cut, independence.