Suppose that a security costs $$3,000$ today and pays off some amount $b$ in one year. Further, suppose that $b$ is uncertain according to the following table of probabilities:

$\backslash$table$[[b_i,$Probability:$],[$$$3,000,0\mathrm{.}1],[,],[$$$3,300,0\mathrm{.}2],[$$$3,600,0\mathrm{.}3],[$$$3,900,0\mathrm{.}2],[$$$4,200,0\mathrm{.}2]]$

a$.$ Calculate the retum $($in percent$)$ for each value of b$.($Note: You may just calculate the total retum and not worry about how this is split up between current yield and capitalgains yield$)($Total Point: $2)$

b$.$ Calculate the expected retum. Show your work. $($Total Point: $2)$

c$.$ Calculate the standard deviations of the return. Show your work. $($Total Point: $2)$

d$.$ Suppose that an investor has a choice between buying this security or purchasing a different security that also costs $$3,000$ today but pays off $$3,300$ with certainty in one year. Explain in words, how an investor's choice of which security to purchase related to his degree of risk aversion in this example.