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We have two vectore of probabilities, $P=\left(p_1,p_2,p_3,p_4\right)$ and $Q=\left(q_1,q_2,q_3,q_4\right)$. Assume that we know only the ralation between $p_i$ and $q_i$. To be more specific we know that $p_1 >q_1, p_4>q_4, p_2<q_2,p_3<q_3$', additionally we can calculate the relations between each pair. I'm interested to know, the relation between entropies of this vectors.

K.D.
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  • I don't understand this question. What do "additionally we can calculate the relations between each pair" and "I'm interested to know, the relation between entropies of this vectors." mean, precisely? – Mateen Ulhaq Jan 18 '18 at 06:40
  • Write $p_i = q_i x_i$. Then substitute that into $P$. Take the entropy of $P$ and $Q$ and compare. – Mateen Ulhaq Jan 18 '18 at 20:03

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