$(2007$ S$2$ Exam, Q$1($e$))$ An investment with return $x$ is a mutual fund consisting of

the shares that make up the Dow Jones Industrial Average. Another investment with

return $Y$ is a mutual fund that is expected to perform best when economic conditions

are weak. Estimates of the returns for each investment $($per $$1,000$ investment$)$

under three economic conditions, each with a given probability of occurrence, are

summarised in the table below.

For this distribution the following summaries are computed:

$E(xY)=-9000,{}_x=$$$121\mathrm{.}35,{}_Y=$$$105\mathrm{.}00.$

$($a$)$ Find the expected returns from each investment.

$($b$)$ Compute the covariance between $x$ and $Y$ and interpret it$.$

$($c$)$ Compare the two investments, is there one we might prefer?