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

  • Thread starter bennyska
  • Start date
  • #1
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Homework Statement


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]

Homework Equations





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.
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
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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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