An x-ray absorbed inside a slab of thickness has a penetration depth (measured from…

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 x-ray absorbed inside a slab of thickness

L = 4\,\mathrm{mm}

has a penetration depth

x

(measured from the front face) that is a continuous random variable with density

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

and

f(x) = 0

outside this range, where

A

is a constant. ((a)) Find

A

and state its units. ((b)) Find the probability that the absorption depth is less than

L/2

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