the standard deviation of the market index portfolio is $10\%.$ stock A has a beta of $2\mathrm{.}50$ and a residual deviation of $20\%.$

a$)$ calculate the total variance for an increase of $0\mathrm{.}10$ in its beta. $($ do not round intermediate calculations$)$

b$)$ calculate the total variance for an increase of $20$ percentage points in its residual standard deviation $($do not round intermediate calculations$)$