Re: [Phys-L] Coincidence Statistics
> John provided the joint probability of two independent event trains which
> occur at a > rate of P=0.1 per second which turns out to be P = 0.009 per
> second.
> This translates to a probability of 0.1 that any 1 second bin will be
> augmented as> calculated below by Alpha
https://imgur.com/gallery/Gd6UXih
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
I had the opportunity to check out a newly announced Large Language Model (LLM)
called Inflection-2 which performs several benchmark tests better than other
LLMs - all except GPT-4 that is.Inflection-2 is invoked in an AI assistant
called Pi
https://pi.ai/talk?utm_source=inflection.ai
I asked for the joint probability of two events whose probability is 0.1 each
and it responded with 0.01.
After presenting it with P joint = (1 - exp(-P1))(1-exp(-P2)) it identified the
formula as an example of Poisson statistics.
P(X = x) = (λ^x) * e^(-λ) / x!
I next asked the probability of exactly one event which it gave as 0.09 soI
infer that the chance of 0,2,3,4... events per time is 0.01
I conclude that I need to express more clearly what I mean by an event train of
0.1 probability per second. Events can be uniformly spaced as from a 0.1 Hz
pulse generator, or they may be randomly spaced like nuclear events, which
still can have a 0.1 probability per second, which uses the symbol lambda, on
an average basis.