Empty Boxes in Random Allocation
Find the exact distribution of empty boxes after a fixed number of random placements.
Free theory articleFind the exact distribution of empty boxes after a fixed number of random placements.
Concept & interpretation
Consider the random placement of n labelled balls into m labelled boxes. If each placement is independent and uniform, there are mn equally likely outcomes in the sample space. This module determines the probability distribution of the number of empty boxes.
Experiment
Follow these steps to observe the exact PMF for varying allocation parameters.
- Select the Boxes control to change the number of boxes. Notice how the total allocations update.
- Adjust the Balls control. Observe the change in the PMF probabilities.
- Change the Empty boxes probe to view the specific exact mass and decimal probability for that value.
For more details, visit https://riano.app/module/occupancy-empty-boxes.