 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability-resit/8/b/i/solution

G_{X + Y} (s) = e^{λ (s - 1)} e^{μ (s - 1)} = e^{(λ + μ) (s - 1)} .

Expanding this last expression as

e^{- (λ + μ)} \sum_{r \geq 0} (λ + μ)^{r} s^{r} / r!

identifies each probability coefficient. Therefore

X + Y \sim Poisson (λ + μ) .

 New to topics? Read the docs here!