A discrete distribution assigns probabilities to a finite set of distinct outcomes. Those outcomes can be binary, categorical, or integer-valued rather than floating-point measurements. Every possible outcome receives a probability, and the probabilities must add up to 1.0. section 3.6 section 3.12
Which controller colors will sell?
Suppose 10,000 controllers sold as follows: black 4,000, gray 3,000, red 1,500, green 700, blue 500, and yellow 300. Dividing each count by 10,000 gives probabilities of 0.40, 0.30, 0.15, 0.07, 0.05, and 0.03. Black is therefore the most likely color for a future sale under this distribution, while all six probabilities together equal 1.0. section 3.6
Table 3.2 Controllers sold and their expected probability
| X |
Controllers sold |
Expected probability P(X) |
|---|---|---|
| BLACK |
4,000 |
4,000 / 10,000 = .4 |
| GREY |
3,000 |
3,000 / 10,000 = .3 |
| RED |
1,500 |
1,500 / 10,000 = .15 |
| GREEN |
700 |
700 / 10,000 = .07 |
| BLUE |
500 |
500 / 10,000 = .05 |
| YELLOW |
300 |
300 / 10,000 = .03 |
Use the table to compare observed controller counts with their corresponding expected probabilities. section 3.6
A bar chart makes the shape easy to inspect because each category gets its own bar. In Python, the same probabilities can be printed, plotted with Matplotlib, or sampled with NumPy's random.choice using the category probabilities. Repeated samples support simple simulations of likely sales outcomes. section 3.6
