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A particle is distributed along the positive x axis with a probability density....

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1. A particle is distributed along the positive x axis with a probability density
P(x) = C x2 exp(-(x/a)2). Determine it's average coordinate <x>, and the fluctuation <&#61508;x2> ; where <&#61508;x>= x-<x>

2. The coordinate of a particle is distributed along the WHOLE x-axis with a probability density
P(x) = C /(x2 +a2)3/2.
Determine C, <x>, and the fluctuation <&#61508;x2>

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The average coordinate of a particle is determined. The solution is detailed and well presented.

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