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Required information Particles are a major component of air pollution in many areas. It is of
interest to study the sizes of contaminating particles. Let X represent the diameter, in
micrometers, of a randomly chosen particle. Assume that in a certain area, the probability density
function of X is inversely proportional to the volume of the particle; that is, assume that f ( x ) =
{ x 3 c 0 x 1 x < 1 where c is a constant. Find the mean particle diameter.

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