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Math Help - Pairwise Independence vs Idependence help

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    Member diddledabble's Avatar
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    Pairwise Independence vs Idependence help

    Okay. I have search the internet over for independence in probability and all I get is pairwise examples. I am trying to figure out exactly what the difference is. For example, what would the formula be to find the  P(A\cup B\cup C) Does it differ from pairwise independence too just finding indepence?
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    Quote Originally Posted by diddledabble View Post
    Okay. I have search the internet over for independence in probability and all I get is pairwise examples. I am trying to figure out exactly what the difference is. For example, what would the formula be to find the  P(A\cup B\cup C) Does it differ from pairwise independence too just finding indepence?
    Here is a standard example.
    Toss a coin twice.
    \mathcal{A} is the event that the first toss yeilds heads.
    \mathcal{B} is the event that the second toss yeilds heads.
    \mathcal{C} is the event that both tosses match (two heads or two tails).

    You can show that \mathcal{A}~\&~\mathcal{B}, \mathcal{A}~\&~\mathcal{C}, and \mathcal{C}~\&~\mathcal{B} are all independent: Pair-wise independence.

    But these are not mutually independent: P\left(\mathcal{A}\mathcal{B}\mathcal{C}\right)\ne P(\mathcal{A})P(\mathcal{B})P(\mathcal{C})
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