Given a list of independent random variables with the same probability density function, we can calculate the probability density function of their maximum and minimum values given their individual probability density functions.

Maximum

Given independent random variables which are evenly distributed with the probability density function the probability density function of their maximum value can be calculated as follows:

Derivation

Via the fundamental theorem of calculus we can then use this to determine the probability density function of the maximum

Minimum

Given independent random variables which are evenly distributed with the probability density function the probability density function of their minimum value can be calculated as follows: