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At 09:47 PM 3/23/00 -0600, Jack Uretsky wrote:
Something is wrong here. Let N_n be the number of occurrences
of n counts in the interval T, and let r be the counting rate. Then,
for a Poisson distribution the total number of counts N is:
N=Sum of n= 0 to infinity of N_n,
where N_n = N{(rT)^n/n!}exp(-rT)
and both the mean and variance of the distribution = rT.
OK.
In other words,
nothing but the total no. of counts depends on N.
I'm not sure what that means. "Nothing" seems like a too-sweeping term.
In this case, r is the probability per unit time that one nucleus
will decay - that in fact is one way to derive the Poisson distribution.
If r is the counting rate (which I take to mean average counting rate) then
don't you mean r/N (not plain r) is the probability per unit time that one
nucleus will decay?