A particle's landing position on a detector strip has density f(x) = 5

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Probability, statistics and stochastic methods · Probability, statistics and stochastic methods

Mathematical Methods for Physics, Ch Probability, random variables and distributions

Problem

A particle's landing position xx on a detector strip has density f(x)=5 m−1,0≤x≤0.2 m,f(x) = 5\,\mathrm{m^{-1}}, \qquad 0 \le x \le 0.2\,\mathrm{m}, and f(x)=0f(x) = 0 outside this range. Someone argues: "this cannot be a valid probability density, because its value, 55, is bigger than 11, and no probability can exceed 11." ((a)) Find the error in this reasoning. ((b)) Given that f(x)f(x) is in fact a valid density, compute P(0.05 m<x<0.15 m)P(0.05\,\mathrm{m} < x < 0.15\,\mathrm{m}).

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