1. 5 ver. 20150415 2. log2log 3. 40% 40% 20% 4. 80% 15% 5% 5. H
= 0.4 log 0.4 0.4 log 0.4 0.2 log 0.2 = 1.52 H0 = 0.8 log 0.8 0.15
log 0.15 0.05 log 0.05 = 0.88 I = H H0 = 0.64bit 6. 7. A B (A, B)
H(A, B) = X ij p(Ai, Bj) log p(Ai, Bj) 8. B1 B2 p(Ai) A1 0.55 0.05
0.6 A2 0.10 0.30 0.40 p(Bi) 0.65 0.35 9. H(A) = 0.6 log 0.6 0.4 log
0.4 = 0.97 10. ABA B 11. AiB A H(B|A) = X i p(Ai)H(B|Ai) = X i
p(Ai) X j p(Bj|Ai) log p(Bj|Ai) = X ij p(Ai, Bj) log p(Bj|Ai) 12.
B1 B2 p(Ai) A1 0.55 0.05 0.60 A2 0.10 0.30 0.40 p(Bi) 0.65 0.35
p(B2|A1) = 0.05 0.6 = 0.08 p(B1|A1) = p(A1, B1) p(A1) = 0.55 0.6 =
0.92 13. B1 B2 p(Ai) A1 0.55 0.05 0.60 A2 0.10 0.30 0.40 p(Bi) 0.65
0.35 p(B2|A1) = 0.05 0.6 = 0.08 p(B1|A1) = p(A1, B1) p(A1) = 0.55
0.6 = 0.92 14. H(B|A) = X i X j p(Ai)p(Bj|Ai) log p(Bj|Ai) = 0.55
log 0.92 0.05 log 0.08 0.1 log 0.25 0.30 log 0.75 = 0.57 I = H(B)
H(B|A) = 0.36 15. H(B|A) = X i X j p(Ai)p(Bj|Ai) log p(Bj|Ai) =
0.55 log 0.92 0.05 log 0.08 0.1 log 0.25 0.30 log 0.75 = 0.57 I =
H(B) H(B|A) = 0.36 16. H(B|A) 0 17. 3 H(A) + H(B) H(A, B) H(A) +
H(B) = X i p(Ai) log p(Ai) X i p(Bj) log p(Bj) = X ij p(Ai, Bj) log
p(Ai) X ij p(Ai, Bj) log p(Bj) = X ij p(Ai, Bj)(log p(Ai) + log
p(Bj)) = X ij p(Ai, Bj)(log p(Ai)p(Bj)) H(A, B) = X ij p(Ai, Bj)
log p(Ai, Bj) 18. x 1 ln x X ij p(Ai, Bj) log p(Ai)p(Bj) X ij p(Ai,
Bj) log p(Ai, Bj) X i pi log qi X i pi log pi X i pi log pi X i pi
log qi 0 X i pi log pi/qi 0 19. logln X ij p(Ai, Bj) log p(Ai)p(Bj)
X ij p(Ai, Bj) log p(Ai, Bj) 20. H(A, B) H(A), H(B) H(A) H(A|B),
H(B) H(B|A) 21. 1.2 22. KL
