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Thread: conditional probability using indicator variable

  1. #1
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    conditional probability using indicator variable

    For an event A, let IA equal 1 if A occurs and let it equal 0 if A does not occur. For a random variable X, show that

    E[X|A] = E[XIA]/P(A)
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  2. #2
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    Re: conditional probability using indicator variable

    this is trivial

    try and do it yourself.
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  3. #3
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    Re: conditional probability using indicator variable

    is it correct to do in this way?
    E(XIA)/P(A)
    =[E(XIA|IA=0)P(IA=0)+E(XIA|IA=1)P(IA=1)]/P(A)
    =[E(X|A)P(A)]/P(A)
    =E(X|A)
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  4. #4
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    Re: conditional probability using indicator variable

    Yes, that is correct. You have used the formula which is known as "total probability" or "the law of iterated expectations".
    Thanks from elmomleo
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