How do I find the probability density function of a random variable X?
This is sort of analogous to various areas of science where one might consider density as mass divided by volume
In physics if one were attempting to find how mass is distributed in an object for something like center of mass they would integrate it
Therein lies the analogy. Just like a physical object is a collection of particles, a probability space is a collection of outcomes.
So, if the probability distribution is described by