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

##### 1 Answer

Oct 27, 2015

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

#f_1(x) " if " a < x < b#

#f_2(x) " if " b < x < c#

# 0 " elsewhere " #

Then cumulative density function (cdf) is defined as

#F(x) =" " 0 " if " x < a #

#F(x)= int_a^ x f(t)" " dt " if " a le x < b#

#F(x) = F(b) + int_b^x f(t) " "dt " if " b le x < c #

#F(x) = 1 " if " x ge c# .

Note that

The cdf just explains how the probability is increasing as we move over the increasing values of