Based on the following information, calculate the expected return and standard deviation for the two stocks:

$\backslash$table$[[,$Rate of return if State Occurs$],[\backslash$table$[[$State of$],[$Economy$]],\backslash$table$[[$Probability of State$],[$of Economy$]],$Stock A$,$Stock B$],[$Recession$,0\mathrm{.}2,0\mathrm{.}04,-0\mathrm{.}15],[$Normal$,0\mathrm{.}3,0\mathrm{.}09,0\mathrm{.}12],[$Boom$,0\mathrm{.}5,0\mathrm{.}17,0\mathrm{.}25]]$

a$)$ If the correlation coefficient between the two stocks is $0.$ And a portfolio invests $50\%$ in Stock A and the rest of the money in Stock B$,$ what is the expected return and standard deviation of the portfolio?

b$)$ Draw the investment opportunity set for all the combinations of the two stocks. Put the standard deviation on the $x-$axis and the expected return on the portfolio on the $Y-$axis. $Yc$ don't have to be accurate on the diagram.

c$)$ If the correlation is $1,$ draw the opportunity set for all the portfolios with the two stocks.