A Geiger counter registers counts at a steady mean rate
PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Data analysis and model fitting in the laboratory
Measurement and Method, Ch Monte Carlo and the bootstrap: uncertainty by sampling
Problem
A Geiger counter registers counts at a steady mean rate R=8.0s−1. The chance of no count occurring in a time t is e−Rt.
((a)) Derive the transformation-method recipe t(ξ) that samples a waiting time between successive counts from a uniform random number ξ on [0,1).
((b)) Use ξ=0.65 to generate one sampled waiting time.
((c)) If 104 such waiting times are generated and the resulting arrivals binned into one-second intervals, state what the mean and the variance of the counts in those bins should come out close to, and why.