Why Does Particle Emission Follow a Poisson Distro?

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Discussion Overview

The discussion revolves around the question of why particle emission is modeled using a Poisson distribution. Participants explore the conditions under which this model applies, particularly in the context of radioactive decay and other particle emission processes.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions the clarity of the original inquiry, noting that the type of particle and the specific property being referenced are not defined.
  • Another participant suggests that the question pertains to particle emission as a Poisson process, explaining that it applies when an event has a constant probability per unit time.
  • A later reply seeks a derivation of the Poisson distribution, acknowledging the initial lack of detail in the question.
  • One participant mentions that the Poisson distribution can be derived from the binomial distribution under certain limits, specifically when the probability of a single event approaches zero and the number of trials approaches infinity.
  • The probabilistic nature of radioactive decay is cited as a reason for its adherence to a Poisson model, emphasizing the importance of having a large sample size.

Areas of Agreement / Disagreement

Participants express differing views on the clarity of the original question and the specific context of particle emission. There is no consensus on the details of the derivation or the applicability of the Poisson distribution to various types of particle emissions.

Contextual Notes

Some assumptions about the types of particles and the properties being discussed remain unspecified, which may affect the applicability of the Poisson model. The discussion also highlights the need for clarity in framing questions related to statistical distributions.

marc.morcos
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Why does particle emission follow a poisson?

Thanks in advance
 
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marc.morcos said:
Why does particle emission follow a poisson?

Thanks in advance

This is a vague question.

What particle? And what property exactly that follows a poisson distribution? I can show you the energy spectrum of beta decay that follows nowhere near a poisson distribution.

If you wish to get some degree of a rational response, you should make some effort into presenting a clear question.

Zz.
 
He probably means that particle emission follows a Poisson process.

If an event has a constant probability per unit time of occurring (i.e., the probability of X happening in the next 10 seconds is always a constant [itex]\lambda[/itex]), then that event can be modeled as a Poisson process. Google it to find a derivation.
 
thanks a lot, sorry about the lack of detail, i was trying to type it before my laptop battery died... what i meant was what ben said. i was looking for the derivation in specific.
 
marc.morcos said:
thanks a lot, sorry about the lack of detail, i was trying to type it before my laptop battery died... what i meant was what ben said. i was looking for the derivation in specific.


The possion distribution is derived from the binomial distribution in with two limits. i. the probability for one event goes to zero and ii. the number of trials goes to infinty. I don't remember it 100%, so better look it up on google or in a reference in introductory statistics. And that is also why one can say (as Ben Niehoff) that the probability is constant [itex]\lambda[/itex]
and so on.

The reason for WHY radioactive decay follow poisson is that is a probibalistic process, and that you have a large sample.
 

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