Radon-222 decays with mean lifetime

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 Estimators and the information in data

Problem

Radon-222 decays with mean lifetime τ=3.8 days\tau = 3.8\,\mathrm{days}. A planned experiment will run for long enough that every decay time is recorded without any truncation, and will collect N=200N = 200 independent decay times. ((a)) State the Fisher information per decay for the exponential lifetime, I(τ)=1/τ2I(\tau) = 1/\tau^2, and evaluate it numerically. ((b)) Compute the total Fisher information IN(τ)=NI(τ)I_N(\tau) = NI(\tau) for the planned experiment. ((c)) Before any data are taken, state the smallest possible standard deviation of an unbiased estimator of τ\tau from this experiment, using the Cramér-Rao bound.

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