 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-3/26k/e/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

k + 1

and rate one. Put

K = \sum_{i = 1}^{n} k_{i} .

X_{1} + \dots + X_{n} \sim Gamma (K + n, 1) .

\prod_{i = 1}^{n} (1 + s)^{- (k_{i} + 1)} = (1 + s)^{- (K + n)} .

f_{X_{1} + \dots + X_{n}} (x) = 1_{{x > 0}} \frac{x ^{K + n - 1} e ^{- x}}{( K + n - 1 )!} .

 New to topics? Read the docs here!