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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

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# Homework Help: Propability Density (I'm stuck need assistance)

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