An electron passing through a thin foil is scattered sideways by a distance with…

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

An electron passing through a thin foil is scattered sideways by a distance

x

with density

f(x) = A\,x(L-x), \qquad 0 \le x \le L,

where

L = 2\,\mathrm{mm}

f(x) = 0

outside this range, and

A

is a constant. ((a)) Find

A

and state its units. ((b)) Find the mean sideways displacement

\langle x\rangle

and the standard deviation of

x

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