A Gaussian input is sampled by acceptance-rejection over the narrower range instead…
PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Data analysis and model fitting in the laboratory · Data analysis and model fitting in the laboratory
Measurement and Method, Ch Monte Carlo and the bootstrap: uncertainty by sampling
Problem
A Gaussian input is sampled by acceptance-rejection over the narrower range ±2σ instead of ±3σ: points are thrown uniformly into a rectangle of width 4σ and height equal to the Gaussian's peak value, and kept if they fall below the curve. The tabulated area of the bell curve within ±2σ is 95.45 per cent of the total. Calculate the fraction of thrown points that is kept.