 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2010/ia/paper-2/12f/b/solution

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

The other marginal is

X_{2} \sim N (μ_{2}, σ_{2}^{2})

by the same square-completion argument with the indices exchanged. Its moment-generating function is therefore

M_{X_{2}} (t) = E [e^{t X_{2}}] = exp (μ_{2} t + \frac{σ _{2}^{2} t ^{2}}{2}), t \in R .

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