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Math Help - Normally distributed random variables

  1. #1
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    Normally distributed random variables

    Not sure about this question, i think the use of letters instead of numbers confuses me. If anyone could provide me with some help, it would be much appreciated

    X is a normally distributed random variable. If a<<b and Pr(X>a)=p and Pr(X<b)=q, find:
    a) Pr(a<X<b)
    b) Pr(X<a/X<b)
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  2. #2
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    Re: Normally distributed random variables

    Quote Originally Posted by gbooker View Post
    X is a normally distributed random variable. If a<<b and Pr(X>a)=p and Pr(X<b)=q, find:
    a) Pr(a<X<b)
    b) Pr(X<a/X<b)
    For part a), \mathcal{P}(X\le a)=1-\mathcal{P}(X>a).
    Do you know how to rewrite \mathcal{P}(a<X<b)~?

    For part b, is that notation suppose to be \mathcal{P}(X<a|X<B)~? OR you you mean \mathcal{P}(X\color{red}>a|X<B)~?
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  3. #3
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    Re: Normally distributed random variables

    [QUOTE=Plato;679274]For part a), \mathcal{P}(X\le a)=1-\mathcal{P}(X>a).
    Do you know how to rewrite \mathcal{P}(a<X<b)~?

    no I can't think of it, I might have learned it, but I just can't remember it at the moment

    For part b, is that notation suppose to be \mathcal{P}(X<a|X<B)~? OR you you mean \mathcal{P}(X\color{red}>a|X<B)~?[/QUOTE

    sorry about the confusion, i meant the first one
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  4. #4
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    Re: Normally distributed random variables

    Quote Originally Posted by gbooker View Post
    Quote Originally Posted by Plato View Post
    For part a), \mathcal{P}(X\le a)=1-\mathcal{P}(X>a).
    Do you know how to rewrite \mathcal{P}(a<X<b)~?

    no I can't think of it, I might have learned it, but I just can't remember it at the moment

    For part b, is that notation suppose to be \mathcal{P}(X<a|X<B)~? OR you you mean \mathcal{P}(X\color{red}>a|X<B)~?
    sorry about the confusion, i meant the first one
    In that case note that (-\infty,a]\cap(-\infty,b]=(-\infty,a]
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