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  1. #13
    ‘Abdü’l-Mecīd-i evvel Member Kival's Avatar
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    Default Re: Logic

    Oh, sorry, I did not want to ask if you have a degree, only if you know enough set theory. Okay, ignore my mistakes in english, I hope you can understand the ideas:

    Okay let's work with set theory then. a is actually quite trivial but I'll try to give you an idea how to prove it:


    Pr(E | H) = Pr(H ∩ E)/Pr(H) (Definition of baysian probability)
    => Pr(H ∩ E) = Pr(E | H)*Pr(H) (just simple transformation)

    As Pr(E | H) has a value range in the interval [0;1] (it's a probability function), obviously it follows:

    Pr(H ∩ E) <= Pr(E | H)*Pr(H)

    Because of Pr(H | E)=Pr(H ∩ E)/Pr(E), the second part of a) follows trivially.

    for b) you just need the equations and knew two things:

    H → ¬E -> (H ∩ E) = {} and Pr ( {} )=0 ({} being the empty set)

    c) Obviously (H ∩ E) and (H^(c) ∩ E) are disjoint sets, so you can use Sigma additivity (H^(c) being the complement of H) . Do you know where to go from there?
    Last edited by Kival; 12-13-2011 at 02:50.

    ‘Abdü’l-Mecīd-i evvel

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