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Finding a combination discrete and continuous cdf to make a new cdf

  1. Jul 1, 2011 #1
    1. The problem statement, all variables and given/known data
    Let F(x)[itex]=\begin{cases}
    .25e^{x} & -\infty<x<0\\
    .5 & 0\leq x\leq1\\
    1-e^{-x} & 1<x<\infty\end{cases}$. Find a CDF of discrete type, F_d(x) and of continuous type, F_c(x) and a number 0<a<1 such that F(x)=aF_d(x)+(1-a)F_c(x)
    [/itex]

    2. Relevant equations



    3. The attempt at a solution
    don't really have any idea of where to begin. i have the answers in the book. any hint would be greatly appreciated.
     
  2. jcsd
  3. Jul 1, 2011 #2

    lanedance

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    Homework Helper

    fc will be continuous, but still will need to be defined explicitly for each interval

    use the discrete probabilities to account for the discontinuities in the current function at x=0,1
     
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