A scintillator counts cosmic-ray muons at a steady rate of and
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
A scintillator counts cosmic-ray muons at a steady rate of 3s−1 and, independently, background gamma rays at a steady rate of 7s−1. Both are Poisson processes and the counter cannot tell which kind of event it has registered, so it records the superposed stream.
((a)) State the rate of the combined counting process and give the probability that the counter is silent for a full 0.05s.
((b)) Find the probability that the counter registers exactly 2 counts in a 0.3s window.