6. (A small world) Consider a world in which there are only two risky assets, A and B,
and a risk-free asset F. The two risky assets are in equal supply in the market; that is,
$M = \frac{1}{2}(A + B)$. The following information is known: $r_F = 0.1$, $\sigma_A^2 = 0.04$, $\sigma_{AB} = 0.01$,
$\sigma_B^2 = 0.02$ and $r_M = 0.18$.
a. Find a general expression (without substituting values) for $\sigma_M^2$, $\beta_A$, and $\beta_B$.
b. According to the CAPM, what are the numerical values of $r_A$ and $r_B$?