A detector records a coincidence with probability per trigger

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Probability, statistics and stochastic methods · Probability, statistics and stochastic methods

Error, Chance and the Machine, Ch Monte Carlo integration and variance reduction

Problem

A detector records a coincidence with probability P=2.0×10−4P = 2.0\times10^{-4} per trigger. This probability is to be estimated by plain Monte Carlo simulation of triggers, counting the coincidences. Using the relative-error formula for a Monte Carlo estimate of a probability, relative error=(1−P)/(NP)\text{relative error} = \sqrt{(1-P)/(NP)}, find the number of simulated triggers NN needed so that the estimate has a relative standard error of 5 per cent.

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