I have a collection of 1000 balls. Some of the balls are light grey, and some are dark grey. All of the light grey balls are exactly the same shade of light grey. Ditto the dark grey ones.
Some of the balls are heavy, and some are light. Again, the heavy ones all weigh exactly the same, and ditto all the light ones.
Balls can be one of 4 types:
- Light grey, light weight
- Light grey, heavy weight
- Dark grey, heavy weight
- Dark grey, light weight
If I were to plot the distribution of these properties on a 2-axis histogram, I would see 4 perfectly sharp spikes, representing these 4 types of ball, no matter what size my bins were. Even if the space were continuous.
What is this type of distribution called in the general N-dimensional case?