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Suppose you are trying to measure the rate of
(total) decay events per second R from
a certain radioactive source using a detector hooked up to a
counter. You put the source in front of the detector and let it
count for 70 seconds, and find that it has measured 537 events in
that 70 s interval. Then you remove the source to measure the
background decay rate (due to noise in the detector and
natural radioactivity), and suppose you now count 211 events in a
90 s interval. Based on these measurements, what is your best
estimate of (while thinking about Poisson Statistics and
propagation of errors):

(a)  the decay rate
R (of the source alone)

(b)  the
uncertainty in R.