 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/8/b/i/solution

For a nonnegative integer-valued random variable

X

G_{X} (s) = E (s^{X}) = j = 0 \sum \infty P (X = j) s^{j}, 0 \leq s \leq 1.

s = 0

, use

0^{0} = 1

G_{X} (0) = P (X = 0)

. The series also converges absolutely for complex

∣ s ∣ \leq 1

; for

s

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