Show that E k 2((k 1) 2) (k 2) (Advice A simple way is to consider a r v U having the 2 k distribution that is, the distribution with parameters (1 2 , k 2 ), and write the integral for

Question: Show that E{ k } = 2((k + 1)/2)/(k/2).(Advice: A simple way is to consider a r.v. U having the 2 k -distribution; that

Show that E{χ_k} = √2Γ((k + 1)/2)/Γ(k/2). (Advice: A simple way is to consider a r.v. U having the χ²_k-distribution; that is, the Γ-distribution with parameters (1/2 , k/2 ), and write the integral for Show that E{χk} = √2Γ((k + 1)/2)/Γ(k/2). (Advice: A simple way is to

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