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Thread: probability questions

  1. #1
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    probability questions

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    Attached Thumbnails Attached Thumbnails probability questions-q-1.jpg   probability questions-q-2.jpg   probability questions-q-3.jpg  
    Last edited by wisdom01; Oct 12th 2017 at 09:25 AM.
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  2. #2
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    Re: probability questions

    Yes. For the first problem, determine each of the following sets:
    $\{\omega: X(\omega) \le 1\}, \left\{\omega: X(\omega) \le \dfrac{1}{4} \right\}, \{\omega: X(\omega) \le 0\}$

    You want to be able to represent each of these sets as an interval or a union of disjoint intervals.
    For (b), you are going to want to do the same thing. Represent the set as an interval or union of disjoint intervals.
    For (c), $F_X$ is not a notation with which I am familiar. How does your book define that?
    For (d), do you really not know how to compute density? That may be something to discuss with your professor.
    For (e), same response.

    For the second one, the problem is fairly straightforward. I am not sure what sort of suggestion to offer until I know why you are having trouble with it.
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  3. #3
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    Re: probability questions

    Quote Originally Posted by SlipEternal View Post
    For (c), $F_X$ is not a notation with which I am familiar. How does your book define that?
    That is not always standard notation. However, it is used by Larson&Marx, because Marx is so influential in mathematical statistics it is used in many textbooks. $F_X(t)=\mathcal{P}(X(t)\le t)$ It is commonly called the cumulative distribution function(Cdf).
    1) $F_X$ is nondecreasing
    2) $F_X$ is continuous on the right.
    3) $\displaystyle{\lim _{t \to - \infty }}{F_X}(t) = 0\quad \& \quad {\lim _{t \to \infty }}{F_X}(t) = 1$
    4) $\mathcal{P}(X<t)=\bf{\lim _{X \to t^-}}{F_X}(t) $
    Last edited by Plato; Oct 12th 2017 at 03:36 PM.
    Thanks from topsquark and SlipEternal
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