Q$12$ Consider the following information: $\backslash$begin$\{$tabular$\}\{|$l$|$c$|$c$|$c$|\}\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$ State of the $\backslash \backslash$ economy $\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$ Probability of $\backslash \backslash$ state of economy $\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$ Return on A $\backslash \backslash \backslash ((\backslash \%)\backslash )\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$ Return on B $\backslash \backslash \backslash ((\backslash \%)\backslash )\backslash$end$\{$tabular$\}\backslash \backslash \backslash$hline Boom & $0\mathrm{.}2$ & $10$ & $5\backslash \backslash \backslash$hline Growth & $0\mathrm{.}3$ & $-2$ & $0\backslash \backslash \backslash$hline Normal & $0\mathrm{.}4$ & $20$ & $15\backslash \backslash \backslash$hline Recession & $0\mathrm{.}1$ & $15$ & $20\backslash \backslash \backslash$hline $\backslash$end$\{$tabular$\}$ a$.$ What is the standard deviation for A$?$ For B$?(5\text{'})$ b$.$ If a new portfolio includes $\backslash (30\backslash \%\backslash )$ in $\backslash (\backslash$mathrm$\{$A$\},30\backslash \%\backslash )$ in B $,$ and $\backslash (40\backslash \%\backslash )$ risk$-$free asset, what is the variance of the new portfolio? $(5\text{'})$