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Propability Density (I'm stuck need assistance)

  1. Dec 12, 2005 #1
    Hi
    I have been given this following problem:
    X is a stochastic variable with the distribution Function F_X which is given by:
    [tex]
    P(X \leq x) = F_{X}(x) = \left\{ \begin{array}{ll}
    0 & \textrm{if} \ x>0 \\
    \frac{{1- e^{-x}}}{{1 - e^{-1}}}& \textrm{if} \ x \in [0,1]\\
    1 & \textrm{if} \ x \geq 1\\
    \end{array} \right.
    [/tex]
    Now I'm supposed to show that X is absolutely continuous and then next calculate the propability density f_x.
    I now then dealing with the propability density is found by
    [tex]F'_{(X)}(x) = \frac{e^{1-x}}{e-1}[/tex]
    But what is the next step from here which will allow me to find the propability density?
    Secondly how do I go about showing that X is absolutly continuous ??
    Sincerely and Best Regards
    Fred
     
    Last edited: Dec 12, 2005
  2. jcsd
  3. Dec 12, 2005 #2
    Hello again,

    My own solution:

    Since [tex]F_{X} (x) [/tex] is differentiable, thereby according to the differention its also continious (but how is it absolutely continious??))

    The density is therefore

    [tex]p(x) = \frac{e^{1-|x|}}{e-1} [/tex]

    Could anyone please inform me if I'm on the right course?

    Best Regards,

    Fred

     
    Last edited: Dec 12, 2005
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