The Poisson Distribution: Derivation

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Here, we derive the Poisson distribution, which shows up in a wide variety of phenomena in science and everyday life. You might want to check out "Why the Poisson Distribution is Important (It's Everywhere!!)"
or
"A Tiny Bit of Combinatorics"
before watching this video.
  1. Think Like a Physicist
  2. poisson distribution
  3. gaussian distribution
  4. probability
  5. statistics
  6. science
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Комментарии
Автор

I have had this explained in class and by many other you tubers with more subscribers than you but noone has been as consice and clear as you. You are a criminally underrated chanel. Thank u.

danielbenton
Автор

Thanks for the video! I find that everyone says that "lambda (or r in this case) * delta_t is the probability", but I can't quite wrap my head around it. How are we interpreting that value as a probability when it's just the expected number of times an event will occur in a given time. @3:59, why is that the probability, conceptually?

Darkev
Автор

Hello, instead of thinking p as r*Δt, and then replacing Δt with T/N, can't we just say that if an event occurs r per unit time in T interval then then its total occurance would be rT and since its the expected value of observing this event then _probability_ of observing _rT_ events out of total _N_ occurances would be *p=rT/N* and now this just becomes a binomial probability problem which can be solved for N→∞

curdyco