 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/discrete-mathematics-continuous-mathematics-and-probability/7/b/i/solution

r, t \geq 0

P (X = r, Y = t) = e^{- (λ + μ)} \frac{λ ^{r} μ ^{t}}{r ! t !} .

It is zero for all other pairs. The factors are the respective Poisson distribution masses, with the product justified by independence.

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