Stocks $x$ and $Y$ have the following probability distributions of expected future returns:

a$)$ Calculate the expected rate of return, hat$(r),$ for Stock Y$.$ Return for Stock X$,(hat(r{)}_x=12\%).$

b$)$ Calculate the standard deviation of expected returns for Stock X$.($That for Stock Y is

$20\mathrm{.}35$ percent.$)$Stocks X and Y have the following probability distributions of expected future returns:

Probability

X

Y

$0\mathrm{.}1$

$-10\%$

$-35\%$

$0\mathrm{.}2$

$2\%$

$0\%$

$0\mathrm{.}4$

$12\%$

$20\%$

$0\mathrm{.}2$

$20\%$

$25\%$

$0\mathrm{.}1$

$38\%$

$45\%$

Calculate the expected rate of return, r $,$ for Stock Y$.$ Return for Stock X$,($rX $=12\%).$

Calculate the standard deviation of expected returns for Stock X$.($That for Stock Y is $20\mathrm{.}35$ percent.$)$