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Prove that the chi-squared distribution is stochastically increasing in its degrees of freedom; that is, p>q, than for any a, P(chi2_p > a) >= P(chi2_q

Prove that the chi-squared distribution is stochastically increasing in its degrees of freedom; that is, p>q, than for any a, P(chi2_p > a) >= P(chi2_q > a), with strict inequality for some a.

Use the results of above to prove that for any v, kF_k,v is stochastically increasing in k.

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