Mixing increases entropy. Show that the entropy of the proba- bility distribution, (P1,..., Pi, Pj, ..,...
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Mixing increases entropy. Show that the entropy of the proba- bility distribution, (P1,..., Pi, Pj, .., Pm), is less than the distribution PitPi of the (P₁,..., Pi+pj 2 2 entropy Pm). Show that in general any transfer of probability that makes the distribution more uniform increases the entropy. 2 Mixing increases entropy. Show that the entropy of the proba- bility distribution, (P1,..., Pi, Pj, .., Pm), is less than the distribution PitPi of the (P₁,..., Pi+pj 2 2 entropy Pm). Show that in general any transfer of probability that makes the distribution more uniform increases the entropy. 2
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