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

1. Jul 1, 2011

### bennyska

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

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. Jul 1, 2011

### 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