# Distribution function primitive

• cham
In summary, the conversation is about finding the cumulative distribution function from a given density function. The person has found the CDF for each interval and noticed that the constants (c) will cancel when integrating. However, their math teacher found a different CDF with c=1/2 and they want to know how c was determined. It is explained that the value of c can be found by setting F(-1) = 0 and F(1) = 1, and it is important to use different symbols for the density function and distribution function to avoid confusion.
cham

## Homework Statement

the distribution function: f(x)=
x + 1 when -1 < x ≤ 0
-x + 1 when 0 ≤ x < 1
0 otherwise

## The Attempt at a Solution

on the first interval i found (1/2)x2 +x + c
on the second interval -(1/2)x2 + x + c
and when integrating the c's will cancel each other

now my math teacher found
on the first inervall f= (1/2)x2 +x+1/2
on the second f=-(1/2)x2 + x +1/2
f=1 otherwise

now i want to know how did find that c=1/2 because we have to draw the graph

Last edited by a moderator:
It's not clearly stated, but I gather you are trying to find the cumulative distribution function from the density function. ('Distribution function' is not specific enough.)
Why do you say the c's cancel? Using the CDF you found for the second interval, including the unknown c, what does that tell you about the CDF at +infinity? What value must a CDF take at +infinity?

cham
cham said:

## Homework Statement

the distribution function: f(x)=
x + 1 when -1 < x ≤ 0
-x + 1 when 0 ≤ x < 1
0 otherwise

## The Attempt at a Solution

on the first interval i found (1/2)x2 +x + c
on the second interval -(1/2)x2 + x + c
and when integrating the c's will cancel each other

now my math teacher found
on the first inervall f= (1/2)x2 +x+1/2
on the second f=-(1/2)x2 + x +1/2
f=1 otherwise

now i want to know how did find that c=1/2 because we have to draw the graph

Please do not use boldface font for the whole message---only for parts you really want to emphasize (as I do below).
Mod note: I removed the excess boldface.
Anyway: you need F(-1) = 0 and F(1) = 1, so that tells you what must be the value of c.

Note: do NOT use the same letter, f, for both the density function and the distribution function; your second function should be called F, or at least by some other symbol different from your first f. Using the same symbol for two different quantities in the same problem is a sure way to lose marks for no good reason!

Last edited by a moderator:
HallsofIvy

## 1. What is a distribution function primitive?

A distribution function primitive is a mathematical function that describes the probability distribution of a random variable. It is used to determine the probability of a random variable falling within a certain range of values.

## 2. How is a distribution function primitive different from a probability density function?

A distribution function primitive gives the probability of a random variable being less than or equal to a specific value, while a probability density function gives the probability of a random variable taking on a specific value.

## 3. What is the purpose of a distribution function primitive?

The main purpose of a distribution function primitive is to provide a way to calculate probabilities for continuous random variables. It is also used in statistical analysis to determine the likelihood of certain outcomes occurring.

## 4. What are some examples of distribution function primitives?

Examples of distribution function primitives include the normal distribution function, the exponential distribution function, and the uniform distribution function. These are commonly used in various fields such as finance, engineering, and social sciences.

## 5. How is a distribution function primitive calculated?

A distribution function primitive is typically calculated using a formula specific to the type of distribution being analyzed. For example, the normal distribution function is calculated using the cumulative distribution function, while the exponential distribution function is calculated using the survival function. These calculations can be done manually or with the help of software or calculators.

Replies
15
Views
1K
Replies
3
Views
3K
Replies
3
Views
1K
Replies
12
Views
1K
Replies
8
Views
790
Replies
7
Views
1K
Replies
7
Views
960
Replies
6
Views
1K
Replies
14
Views
1K
Replies
10
Views
4K