Poisson Thinning and Independent Counts

Split Poisson arrivals into two types by independent Bernoulli marking and verify that the resulting retained and rejected counts are independent Poisson random variables.

Interactive Experiment

This interactive experiment allows you to visually and computationally verify that splitting a Poisson process yields two independent Poisson processes.

1. Open the Poisson Thinning module.
2. Set the Poisson mean to 4 and Retention quarters to 1 (p = 1/4).
3. Observe that the Marginal Means update to 1 for Retained and 3 for Rejected.
4. Set the Retained count to 1 and the Rejected count to 2, and verify that Joint P(R=1, J=2) equals the product of the marginals while Cov(R, J) remains 0.