Re: [問題] 條件機率
※ 引述《KevinXII ()》之銘言：
: 請問一下
: Prove or Disprove:
: (a)Suppose A and B are independent events. Then A and B are conditional
: independent given C, where P(C)>0, i.e. P(AB|C) = P(A|C)P(B|C).
否 令Ω={1,2,3,4}, A={1,2}, B={1,3}. C{1,4}
P(AB|C)=P(ABC)/P(C)=(1/4)/(1/2)=1/2
P(A|C)=P(AC)/P(C)=(1/4)/(1/2)=1/2
P(B|C)=P(BC)/P(C)=(1/4)/(1/2)=1/2
P(AB|C)=1/2≠P(A|C)P(B|C)=1/4
: (b)If P(A)>P(B), then P(A|C > P(B|C), where P(C)>0.
題目 應該是 If P(A)>P(B), then P(A|C)>P(B|C), where P(C)>0 吧！
否 令Ω={1,2,3,4}, B=C={1,2}, A={1,3,4}
則P(A)=3/4 > P(B)=1/2 但 P(A|C)=1/2 < P(B|C)=1,
所以 若P(A)=P(B), 則P(A|C)>P(B|C)的敘述未必成立
: 麻煩各位高手了
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: 謝謝~~
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