請問Bonferron Inequaloity的統計証明題~

試用數學歸納法來証或其它方法來証

P(A1交集A2交集A3交集...交集An)>=[P(A1)+P(A2)+...P(An)-(n-1)]

越祥細越好~請加祥細說明謝謝~我的數學不是很好

3 個解答

評分
  • Eric
    Lv 6
    1 0 年前
    最佳解答

    Proof.

    Basis. P(A1∩A2) = P(A1) + P(A2) - P(A1∪A2) ≥ P(A1) + P(A2) - 1, so the claim holds for the case n = 2.

    Induction. Suppose the claim holds for some n ≥ 2. Then

    P(A1∩A2∩...∩An∩An+1) ≥ P(A1∩A2∩...∩An) + P(An+1) - 1 (from the n = 2 case already proven)

    ≥ P(A1) + ... + P(An) - (n-1) + P(An+1) - 1 (from the inductive hypothesis)

    = P(A1) + ... + P(An) + P(An+1) - ((n+1)-1),

    so the claim holds for n+1.

    By induction, the claim holds for all n ≥ 2.

  • 1 0 年前

    你的 IE 是第幾版。舊版的就改用 7.0 版。

  • sorry~some place I can't see, just like n 2 and (... ) ?sign (... )

    2007-07-09 12:35:51 補充:

    P(A1∪A2) ??? P(A1)

    2007-07-11 13:00:19 補充:

    that's right~

還有問題?馬上發問,尋求解答。