A cube-shaped sample has edge length

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Uncertainty in measurement

Scientific Computing for Physicists, Ch The uncertainty of a simulated number: inputs, sensitivity and correlated output

Problem

x = 2.00 \pm 0.02\,\mathrm{m}

, an epistemic uncertainty in a fixed edge, evaluated Type B from the calliper's resolution. Its volume is

y = x^3

. ((a)) Propagate the uncertainty linearly to obtain

y_0

and

u_y

. ((b)) The mean of

y

under Monte Carlo sampling shifts from

y_0

by approximately

3x_0 u_x^2

(from expanding

(x_0+\delta)^3

and keeping

\mathrm{E}[\delta^2] = u_x^2

). Compute this shift as a fraction of

y_0

, and say whether Monte Carlo propagation would disagree noticeably with the linear result.

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