6.1.3—Poisson distribution

Independent Poisson variables add to a Poisson variable: if X~Po(λ₁) and Y~Po(λ₂), then X+Y~Po(λ₁+λ₂).

Check independence and compatible exposure definitions before combining. For a difference or conditional count, the simple sum rule does not apply.

Counts from two independent sensors with means 2 and 3 per hour combine to Po(5) per hour.

Adding observed counts is always possible, but adding Poisson distributions requires independence and parameter interpretation.