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

[bennyska]

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.

 

[lanedance]

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