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

• bennyska
In summary, the conversation revolved around finding a CDF of discrete and continuous type for a given function and a constant value "a". The solution is to define the continuous CDF separately for each interval and use the discrete probabilities to account for the discontinuities at x=0 and x=1.
bennyska

## 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.

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

## 1. What is a combination discrete and continuous cdf?

A combination discrete and continuous cdf is a cumulative distribution function that combines both discrete and continuous variables. It is used to determine the probability of a random variable falling within a certain range of values.

## 2. Why would someone want to find a combination discrete and continuous cdf?

A combination discrete and continuous cdf is useful when working with data that contains both discrete and continuous variables. It allows for a more accurate representation of the data and can provide more precise probability calculations.

## 3. How do you create a combination discrete and continuous cdf?

To create a combination discrete and continuous cdf, you must first determine the individual cdfs for the discrete and continuous variables. Then, you can combine them using the appropriate formula, such as the addition rule for probabilities.

## 4. What are the benefits of using a combination discrete and continuous cdf?

Using a combination discrete and continuous cdf allows for a more comprehensive analysis of data that contains both discrete and continuous variables. It also provides a more accurate representation of the data, leading to more precise probability calculations.

## 5. Can a combination discrete and continuous cdf be used for any type of data?

Yes, a combination discrete and continuous cdf can be used for any type of data that contains both discrete and continuous variables. It is a versatile tool that can be applied in various scientific fields, such as statistics, physics, and engineering.

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