 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-2/4f/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

f (x_{1}, x_{2}) = \frac{1}{2 π σ _{1} σ _{2} 1 - ρ ^{2}} exp {- \frac{1}{2 ( 1 - ρ ^{2} )} [\frac{( x _{1} - μ _{1} ) ^{2}}{σ _{1}^{2}} - \frac{2 ρ ( x _{1} - μ _{1} ) ( x _{2} - μ _{2} )}{σ _{1} σ _{2}} + \frac{( x _{2} - μ _{2} ) ^{2}}{σ _{2}^{2}}]} .

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