 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability-resit/9/a/i/solution

λ > 0

, the probability mass function is

P (X = k) = e^{- λ} \frac{λ ^{k}}{k !}, k = 0, 1, 2, \dots,

and is zero at all other values. Its normalization follows from the exponential series

\sum_{k \geq 0} λ^{k} / k! = e^{λ}

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