Barbara Szwal

Grupa I1E1S1

V_P = w₁²s₁² + w₂²s₂² + 2w₁w₂s₁s₂ρ₁₂

Po podstawieniu w₂ = 1 − w₁ obliczeniu pochodnej po w₁ i przyrównaniu do zera otrzymujemy:

$$V_{P} = \frac{s_{1}^{2}s_{2}^{2}(1 - \rho_{12}^{2})}{s_{1}^{2} + s_{2}^{2} - 2s_{1}s_{2}\rho_{12}}$$

$$w_{1} = \frac{s_{2}^{2} - s_{1}s_{2}\rho_{12}}{s_{1}^{2} + s_{2}^{2} - 2s_{1}s_{2}\rho_{12}}$$

$$w_{2} = \frac{s_{1}^{2} - s_{1}s_{2}\rho_{12}}{s_{1}^{2} + s_{2}^{2} - 2s_{1}s_{2}\rho_{12}}$$