The estimated linear probability model used by a financial institution to predict business loan applicant default probabilities is given by:

P D$=0\mathrm{.}03$ X$\_1+0\mathrm{.}02$ X$\_2-0\mathrm{.}05$ X$\_3+$ error

where X$\_1$ is the borrower's debt$/$equity ratio X$\_2$ is the volatility of borrower earnings, and X$\_3$ is the borrower's profit margin. For prospective borrower A: For prospective borrower B X$\_1=0\mathrm{.}80,$ X$\_2=0\mathrm{.}20,$ and X$\_3=0\mathrm{.}15.$ Calculate the expected probabilities of default $($PD$)$ for each prospective borrower and discuss which borrower is the better loan candidate. $(8$ marks$)$ Explain the major weaknesses of the linear probability model. $(2$ marks$)$