In the case you solved Exercise 36, find the mean speed of a molecule. (Advice: Use the

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In the case you solved Exercise 36, find the mean speed of a molecule. (Advice: Use the fact that Γ(t +1) = tΓ(t).)


Exercise 36

Show that E{χk} = √2Γ((k + 1)/2)/Γ(k/2). (Advice: A simple way is to consider a r.v. U having the χ2-distribution; that is, the Γ-distribution with parameters (1/2 , k/2 ), and write the integral forimage

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