A capacitor is specified as lying uniformly between and

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Data analysis and model fitting in the laboratory

Measurement and Method, Ch Monte Carlo and the bootstrap: uncertainty by sampling

Problem

A capacitor is specified as lying uniformly between

220\,\mathrm{pF}

and

260\,\mathrm{pF}

, so its capacitance can be written as the best estimate

240\,\mathrm{pF}

plus a rectangular contribution of half-width

a = 20\,\mathrm{pF}

. ((a)) Write the transformation-method recipe that turns a uniform random number

\xi

[0,1)

into a sampled value of the capacitance

C

. ((b)) Using

\xi = 0.638

, generate one sampled value of

C

. ((c)) State the standard deviation expected of

10^4

such samples, and compare it with

a/\sqrt{3}

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