 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2005/ii/paper-4/13i/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

ν > 0

and rate

ν / μ_{i}

, requiring

μ_{i} > 0

. Direct integration gives

E (Y_{i}^{r}) = (\frac{μ _{i}}{ν})^{r} \frac{Γ ( ν + r )}{Γ ( ν )}

for

ν + r > 0

. Using

Γ (ν + 1) = ν Γ (ν)

and

Γ (ν + 2) = ν (ν + 1) Γ (ν)

E Y_{i} = μ_{i}, var Y_{i} = μ_{i}^{2} / ν .

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