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

## Homework Statement

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

## 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

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lanedance
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