Show that, for any law of distribution of molecular speeds, [ left{langle uangleleftlanglefrac{1}{u}ightangleight} geq 1 ] Check

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Show that, for any law of distribution of molecular speeds,

\[
\left\{\langle uangle\left\langle\frac{1}{u}ightangleight\} \geq 1
\]

Check that the value of this quantity for the Maxwellian distribution is \(4 / \pi\).

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