Merging and Splitting of a Poisson Process

Instructions

Two independent Poisson emitters operate at rates \(\lambda_1\) and \(\lambda_2\).
Merge: Combines both streams into one with rate \(\lambda_1 + \lambda_2\). The moment of merging is marked on the line chart.
Adjust \(\lambda_1\) and \(\lambda_2\) using the sliders. Click “Merge” to see the effect, and "Reset & Split" to revert.
Left Panel: Visualizes emitters merging and splitting.
Right Panel: Two real-time charts:
1. Live line chart: emissions per second.
2. Histogram: empirical probability of emission counts vs the theoretical PMF.
Observations Panel: Tracks the running average emission rate vs the theoretical rate \(\lambda\).

\(\lambda_1\) (Emitter 1): 10

\(\lambda_2\) (Emitter 2): 5

Action: