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Boltzmann distribution for particle energy

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I'm puzzled by the appearance in the literature of 2 conflicting forms:

P(E)=√(E)*exp(-E), which I understand as derived from the Maxwell distribution for speed.
It is a chi -square distribution with 3 degrees of freedom.

P(E)=exp(-E), which seems wrong to me.

But it is not simply a mistake because numerous reputable sources give each form. What is the relationship?

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