Cosmic-ray muons arrive at sea level at a rate of about integrated over all directions
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Probability, statistics and stochastic methods · Probability, statistics and stochastic methods
Error, Chance and the Machine, Ch Random processes in continuous time
Problem
Cosmic-ray muons arrive at sea level at a rate of about 1cm−2min−1 integrated over all directions, a standard order-of-magnitude figure for the rate through a horizontal detector. A scintillator counter of area 200cm2 registers these muons as the clicks of a Poisson process. The counter has a non-paralysable dead time of 2μs: a true arrival during the dead time after a recorded click is simply not registered, and does not itself extend the dead time.
((a)) Estimate the counter's mean recorded counting rate.
((b)) Estimate the fraction of true arrivals lost to dead time.
((c)) Estimate how many muons are missed over a 24hour run.