Re: statistical fluctuations

[Bernard Cleyet <anngeorg@PACBELL.NET>]

Sorry, I read too quickly.


I do think so.  To verify use the binomial distribution and compare with
the Poisson.  the P. distrib. applies when the probability of occurrence
is very small p << 1. [and ....]

i.e.   SD^2 = m(1-p), while for Poisson:   SD^2 = m       [p is
probability of event occurrence, zero to one; m is mean, i.e. pz
probability of occurrence times number of trials].  Here p is
proportional to the half life X number of nuclei X the efficiency of the
detector.  Since I assume the half life is long and the number large
(also satisfies the requirement the number of nuclei doesn't change
during the measurement), I think the P distribution applies.   However,
at such a low rate, ten, its value being the mean is rather unlikely.
i.e. the probability of its being 10 or 9 are about the same and less
than 15%, assuming the "actual" value is ten.  I'm too lazy to calculate
the values, so I've taken them approximately from Taylor (An Intro. to
Error Analysis) who has a histogram for m = 9.

bc

Ludwik Kowalski wrote:

> In a private message  Bernard Cleyet asked:
>
> > p.s. why "stat. flucts."?=A0 I think subtracting
> > background is more appropriate.
>
> In my illustration one chip recorded 47 tracks
> (signal plus background) while another recorded
> 37 (background). I subtract and obtain signal
> equal to 10. But I can not say that signal=3D10
> because both 47 and 37 would fluctuate from
> chip to chip. The probability that the true signal
> is 10 is very very small in this example.
>
> Now consider the Oriani's method. (His numbers
> were actually much larger, I made them small to
> focus on fluctuations. Suppose that  using his
> method (one chip) I observe 37 before the
> experiment and 47 after the experiment. I conclude
> that the signal is 10. Yes, I do not expect that the next
> experiment will yield the same signal but the result
> will always be positive or zero. Is it correct to say
> that the standard deviation for the signal should
> be sqrt(10), in this illustration? I am not certain.
> Ludwik Kowalski