$2.$ You have $$10,000$ saved up to invest for a year and are considering stocks $($S$)$ and$/$or short$-$term Treasury bills $($T$).$ The returns from both sources are judged uncertain, of course, as the following probability table indicates:

a$.$ If you split your investment $30\%$ in stock and $70\%$ in Treasury bills, what would be the expected return and standard deviation? $(10$ points$)$

b$.$ Are the return of stock and bond independent? $(10$ points$)$