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.