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conditional independence chp13

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  • meskabnada
    Hi, In the book p.482 it is mentioned that the full joint distribution table has seven independent members (2*2*2 - 1 because the number must sum to 1). I
    Message 1 of 2 , May 18, 2008
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      Hi,
      In the book p.482 it is mentioned that the full joint distribution
      table has seven independent members (2*2*2 - 1 because the number must
      sum to 1). I didn't understand why it is 7. the provided explanation is
      not clear for me.

      Thanks for you cooperation

      zayan
    • Peter Norvig
      It might be easier to think of it as 8 values. For example, these might be the eight values: [.2, .2, .1, .1, .1, .1 .1, .1] Notice that these sum to 1.0
      Message 2 of 2 , May 20, 2008
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        It might be easier to think of it as 8 values.  For example, these might be the eight values:

            [.2, .2, .1, .1, .1, .1 .1, .1]

        Notice that these sum to 1.0 (since they are mmutually exclusive and exhaustive possibilities).  Because we know they sum to 1.0, if we know the first 7, we must know the last one.  The first 7 sum to .9, so the last one must be .1.  Therefore, if we want to save space, we can drop the last one:

            [.2, .2, .1, .1, .1, .1 .1]

        There are 7 values, and we can derive the fact that the missing 8th value must be .1.

        -Peter

        On Sun, May 18, 2008 at 2:53 AM, meskabnada <meskabnada@...> wrote:
        Hi,
        In the book p.482 it is mentioned that the full joint distribution
        table has seven independent members (2*2*2 - 1 because the number must
        sum to 1). I didn't understand why it is 7. the provided explanation is
        not clear for me.

        Thanks for you cooperation

        zayan


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