How do you derive a cumulative density function from a probability density function?
Finding the cumulative density function is a process of integrating the pdf over different intervals over which the random variable is defined.
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#.
The cdf just explains how the probability is increasing as we move over the increasing values of