A person is interested in constructing a portfolio. Two stocks are being considered. Let $x=$ percent return for an investment in stock $1,$ and $y=$ percent return for an investment in stock $2.$ The expected return and variance for stock $1$ are $E(x)=8\mathrm{.}45\%$ and Var$(x)=25.$ The expected return and variance for stock $2$ are $E(y)=3\mathrm{.}20\%$ and Var$(y)=1.$ The covariance between the returns is ${}_{xy}=-3.$

$($a$)$ What is the standard deviation $($as a percent$)$ for an investment in stock $1?$

$\%$

What is the standard deviation $($as a percent$)$ for an investment in stock $2?$

$\%$

Using the standard deviation as a measure of risk, which of these stocks is the riskier investment?

An investment in stock $1|$ be risky compared with an investment in stock $2.$

$($b$)$ What is the expected return and standard deviation, in dollars, for a person who invests $$600$ in stock $1?$

expected return

$

standard deviation

$($c$)$ What is the expected percent return and standard deviation, in dollars, for a person who constructs a portfolio by investing $$300$ in each stock? $($Round your answer for standard deviation to two decimal places.$)$

expected return

$

standard deviation

$

$($d$)$ What is the expected percent return and standard deviation for a person who constructs a portfolio by investing $$420$ in stock $1$ and $$180$ in stock $2?($Round your answer for standard deviation to two decimal places.$)$

expected return

$

standard deviation

$($e$)$ Compute the correlation coefficient for $x$ and $y.$

Comment on the relationship between the returns for the two stocks.

There is

relationship between the variables.