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Math Help - Marginal Distribution

  1. #1
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    Marginal Distribution

    Hi,

    I am unsure whether my arguments below are correct.

    Suppose that P(A, B, C) is a discrete joint distribution. My goal is to express P(A | B) in terms of P(A | B, C).

    My solution:

    P(A | B) =  \dfrac{P(A \cap B)}{P(B)}
    P(A | B) = \sum_c \dfrac{P(A \cap B \cap \{c\})}{P(B)} = \sum_c \dfrac{P(A, B |\{c\})}{P(B)}P(\{c\}) = \sum_c P(A | B, \{c\})P(\{c\})

    Thanks and best regards,

    samosa
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  2. #2
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    Re: Marginal Distribution

    Hey samosa.

    This looks pretty good.
    Thanks from samosa
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  3. #3
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    Re: Marginal Distribution

    Hi Chiro,

    thanks a lot for your help.

    Best,

    samosa
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