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For questions about probability, probability theory, probability distributions, expected values and related matters. Purely mathematical questions should be asked on Math.SE.

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Understanding $\mathrm dP_x$ in the derivation of Maxwell-Boltzmann distribution

If we don’t, the probability would be zero. This probability is proportional to the range $\mathrm du_x$. … Maxwell, based on probability theory, deduced that it is also proportional to $\mathrm e^{-\frac\beta3}$ or $\mathrm e^{-\frac{\beta u^2}2}$, where $\beta$ is a constant. …
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