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There is a probability distribution: $$p(x) = a \,x^2\, \exp( -b\,x^2 ), \quad a,b>0,\ x \in ( -\infty,\,\infty ) $$ I wonder which probability distribution is it?

Lyn
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1 Answers1

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With the correct scaling it is the http://en.wikipedia.org/wiki/Maxwell_distribution

gammatester
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  • I forgot to mension $x \in ( -\infty,,\infty )$. Does it still belong to Maxwell-Boltzmann distribution? – Lyn Jul 28 '14 at 13:38
  • I don't think so. But are you sure that in your context negative $x$ are meaningful? (The PDF is an even function.) – gammatester Jul 28 '14 at 13:52