Z x y x y 0 i x y 0 i x y z 4 6

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Unformatted text preview: ‪ q‬על שלושה ערכים כך ש 0 = )‪.D (p||q ) = D (q ||p‬‬ ‫1‬ ‫פתרון אפשרי: 1 , 1 , 1 = ‪P = 4 , 1 , 1 , Q‬‬ ‫24‬ ‫424‬ ‫3‬ ‫אנטרופיה של סכום‬ ‫יהי ‪ X‬משתנה מקרי המקבל את ערכיו ב־ ‪ x1 , ..., xr‬ו־ ‪ Y‬מ"מ המקבל את ערכין ב־ ‪.y1 , ..., ys‬‬ ‫נגדיר ‪.Z = X + Y‬‬ ‫1. הראו כי מתקיים: ) ‪H (Z | X ) = H (Y | X‬‬ ‫פתרון: ‪ Z = X + Y‬ולכן: )‪.p (Z = z | X = x) = p (Y = z − x | X = x‬‬ ‫)‪p (x) H (Z | X = x‬‬ ‫)‪p (Z = z | X = x) log p (Z = z | X = x‬‬ ‫−=‬ ‫)‪p ( x‬‬ ‫‪z...
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This document was uploaded on 03/20/2014 for the course CS 67548 at Hebrew University of Jerusalem.

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