How do you derive a cumulative density function from a

hionormf

hionormf

Answered question

2022-01-16

How do you derive a cumulative density function from a probability density function?

Answer & Explanation

Neunassauk8

Neunassauk8

Beginner2022-01-16Added 30 answers

Finding the cumulative density function is a process of integrating the pdf over different intervals over which the random variable is defined.
Explanation:
Consider probability density function (pdf) defined as
f1(x) if a<x<b
f2(x) if b<x<c
0 elsewhere
Then cumulative density function (cdf) is defined as
F(x)=0 if x<a
F(x)=axf(t)dt if ax<b
F(x)=F(b)+bxf(t)dt if bx<c
F(x)=1 if xc.
Note that F(b)=abf1(t)dt
The cdf just explains how the probability is increasing as we move over the increasing values of x.

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