9. (15%) Sketch the region of integration and write an equivalent integral with the order of integration reversed. Then evaluate both integrals. ∫_0^3/2 ∫_-√9-4y^2^√9-4y^2 y dx dy.

I. (10%) A stock portfolio is composed of two stocks: \( A_{1} \) and \( B_{1} \). Another stock portfolio also has two investments: stocks \( A_{2} \) and \( B_{2} \). Suppose the mean prices \( (\mu) \) and the standard deviations \( (\sigma) \) of \( A_{1} \) and \( A_{2} \) are equal, and the mean price and standard deviation of \( B_{1} \) are equal to those of \( B_{2} \) (i.e., \( \mu_{A_1} = \mu_{A_2}, \mu_{B_1} = \mu_{B_2}, \sigma_{A_1} = \sigma_{A_2}, \sigma_{B_1} = \sigma_{B_2} \)). Suppose each stock comprises 50% of the portfolio. However, the correlation between stocks is higher in the first portfolio (i.e., \( \rho_1 > \rho_2 \)). Explain the difference in expected returns and risks between the two portfolios.

9. (15%) Sketch the region of integration and write an equivalent integral with the order of integration reversed. Then evaluate both integrals. $$\int_0^{3/2} \int_{-\sqrt{9-4y^2}}^{\sqrt{9-4y^2}} y \, dx \, dy.$$

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