Re: [Phys-L] Coincidence Statistics
[Paul Nord]
> I'm looking at a lab writeup that suggests the coincidence rate Rc will be
> a function of the two rates (R1 and R2) and the timing resolution (t).
>
> Rc = R1*R2*t
>
> In my case:
> Rc = 0.1 * 0.1 * 1
> or 1 event every 100 seconds
[John Denker]
I assume the definition of coincidence is one or more counts in the
channel 1 *and* one or more counts in channel 2, in a particular small
bin.
The chance of one or more is 1 minus the chance of zero, which is easy
to calculate from the standard Poisson formula. So
Pc = (1 - exp(-R1))(1 - exp(-R2))
When both rates are small, that reduces to the product R1 R2.
More generally you need the full equation [1].
****************************************************************************
[Brian W]
Here is a graphical representation, showing the joint probability of two 0.1 P
events is a little less than 0.01
https://imgur.com/a/eqB4PHb
(credit Wolfram Alpha)