3 ms·

I've had this discussion with a professional mathematician. As unintuitive as it does sound, actually random independent events are more likely to follow after

• _yb2s 2y ago
  You as misinterpreting their reply. The fact that the Poisson distribution falls off exponentially is because the longer you wait, the more likely that the very next event has already happened. Once an event happens, that specific event cannot happen again so the probability is low after long distances and/or time intervals. This effect only shows up when you are looking at the probabilities of individual events- when you look at the aggregate results after a long time, they are totally random, and no more likely to occur next to one another. The exponential nature of the Poisson distribution does not cause any clumping. If you survive a plane crash, you are still no more likely to survive another plane crash than a regular person, unless you do something else that makes it no longer independent, and therefore no longer following the same Poisson distribution as everyone else (e.g. you fly a lot). However, assuming standard behavior, if you do get in a plane crash, you are more likely to get in your very next plane crash in the next year, than in year 10. However, a person never in a plane crash is also equally more likely to get in their first plane crash in the next year than 10 years out. And you are still just as likely to get in a plane crash in year 10, just not your next one. Poisson clumping is just a result of human bias-sort of like an optical illusion. We incorrectly expect random things to be evenly spaced. Music players with random shuffle for example, will often seem to play the same song over and over, and will only feel 'random' when they are modified to be non-random such that they avoid playing the same song within some time interval.