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Math Help - Normal Distribution

  1. #1
    Junior Member Kanwar245's Avatar
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    Normal Distribution

    Suppose X ~ N(0,1).
    Why can we write P(a≤ X ≤ b) = P(X ≤ b) P(X ≤ a)
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  2. #2
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    Re: Normal Distribution

    Quote Originally Posted by Kanwar245 View Post
    Suppose X ~ N(0,1).
    Why can we write P(a≤ X ≤ b) = P(X ≤ b) P(X ≤ a)
    To really answer your question, we need to know how much you understand about continuous distributions.
    For example do you understand that for any a, \mathcal{P}(X=a)=0~?
    From that it follows at once that \mathcal{P}(X\le a)=\mathcal{P}(X<a).
    So \mathcal{P}(X\ge a)=1-\mathcal{P}(X<a)=1-\mathcal{P}(X\le a).

    Thus =\mathcal{P}(a\le X \le b)=\mathcal{P}(X\le b)-\mathcal{P}(X\le a).
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