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

[bennyska]

Homework Statement

Let F(x)=\begin{cases}<br /> .25e^{x} &amp; -\infty&lt;x&lt;0\\<br /> .5 &amp; 0\leq x\leq1\\<br /> 1-e^{-x} &amp; 1&lt;x&lt;\infty\end{cases}$. Find a CDF of discrete type, <i>F_d(x)</i> and of continuous type, <i>F_c(x)</i> and a number 0&lt;a&lt;1 such that <i>F(x)</i>=aF_d(x)+(1-a)F_c(x)<br />

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