Say there is a random variable
X which can take 3 values
3 with equal probability. The task is to draw realizations from this random variable.
Any simple textbook will say consider a realization as
1 if you get a realization from Uniform distribution as less than, 0.33, and as
2 if you get a realization from Uniform distribution as less than, 0.66 (and more than 0.33), and otherwise
This is okay, however, I could not understand the logic of it. I understand that logically it is somehow related to the fact that the CDF of all random variable has a uniform distribution, however, I could not establish the link between above drawing policy and this CDF's distributional theory.
Could somebody please explain this to me in an intuitive way?