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The naïve solution to this paradox is to calculate a pvalue
using only the bin presenting the highest fluctuation. This approach would give
a very small number (
) in our 1000 bin example, and would
remain below the threshold even if the spike has only 5 events over
a background of 1.
Applying this reasoning to the ROG data we get

(2) 
a pvalue which may be considered `significative'. (Note that, if we used the observed
background of Fig. 1, that we do not believe it is the correct number
to use, the pvalue would be
.)
Giulio D'Agostini
20050109