$1.$A$.)$ Financial analysts have estimated the returns on shares of the Woods Corporation and the overall market portfolio under two economic states nature as follows. For Woods the state dependent returns are $-0\mathrm{.}02$ in recession, and $0\mathrm{.}06$ in an economic boom. For the market the state dependent returns are $-0\mathrm{.}06$ in recession, and $0\mathrm{.}12$ in boom. The analyst estimates that the probability of a recession is $0\mathrm{.}50$ while the probability of an economic boom is $0\mathrm{.}50.$ Compute the standard deviation of the market. B$.)$ Financial analysts have estimated the returns on shares of the Woods Corporation and the overall market portfolio under two economic states nature as follows. For Woods the state dependent returns are $-0\mathrm{.}01$ in recession, and $0\mathrm{.}06$ in an economic boom. For the market the state dependent returns are $-0\mathrm{.}04$ in recession, and $0\mathrm{.}12$ in boom. The analyst estimates that the probability of a recession is $0\mathrm{.}50$ while the probability of an economic boom is $0\mathrm{.}50.$ Calculate the beta of Woods. C$.)$ Financial analysts have estimated the returns on shares of the Goldday Corporation and the overall market portfolio under two economic states nature as follows. For Goldday the state dependent returns are $-0\mathrm{.}04$ in recession, and $0\mathrm{.}06$ in an economic boom. For the market the state dependent returns are $-0\mathrm{.}12$ in recession,and $0\mathrm{.}18$ in boom. The analyst estimates that the probability of a recession is $0\mathrm{.}50$ while the probability of an economic boom is $0\mathrm{.}50.$ Compute the covariance between Goldday and the market. D$.)$ Financial analysts have estimated the returns on shares of the Goldday Corporation and the overall market portfolio under two economic states nature as follows. For Goldday the state dependent returns are $-0\mathrm{.}06$ in recession, and $0\mathrm{.}06$ in an economic boom. For the market the state dependent returns are $-0\mathrm{.}06$ in recession,and $0\mathrm{.}16$ in boom. The analyst estimates that the probability of a recession is $0\mathrm{.}50$ while the probability of an economic boom is $0\mathrm{.}50.$ Compute the standard deviation of the market.