Exercise 3.3 Suppose that X Poi(), Y Poi() and they are independent. Using the MGF

Exercise 3.3 Suppose that X ∼ Poi(λ), Y ∼ Poi(μ) and they are independent.

Using the MGF of Poisson distributions, show that X+Y ∼ Poi(λ+μ).

Interpret this result in terms of Bernoulli trials.