What is the Uniform Distribution?
Also, what is a distribution?
I thought long and hard about how to introduce the concept of a probability distribution to folks, and I thought it best to start with a simple example, and we can work up to the general definitions later.
But for now, it’s best to think of a probability distribution as a random number generator with special properties. There’s a boatload of different types of distribution but we’ll start with one of the simpler ones.
A Uniform distribution is defined by two numbers a and b and is usually written as U[a,b] where U stand for ‘Uniform’, and a and b are any two (real*) numbers.
When you generate a number from the U[a,b] distribution, you will get a random number between a and b (inclusive) where any number between a and b has an equal (or uniform) probability of being drawn.
The Uniform distribution comes in both discrete and continuous flavours and can be used to generate a ‘fair’ number given two defined endpoints.
When you roll a D6, you are effectively sampling from a discrete uniform distribution with a = 1 and b = 6. You are realising a random variable from which is distributed as U[1,6].
RPGs and Gacha systems use Uniform random numbers to power their systems, but there are more interesting distributions to use for other situations!
*Don’t know what a ‘real’ number is? Don’t worry about it (yet)