Consider two local banks. Bank A has $110$ loans$$ outstanding, each for $$$$0\mathrm{.}4$million$,$ that it expects will be repaid today. Each loan has a $10\%$ probability of$$ default, in which case the bank is not repaid anything. The chance of default is independent across all the loans. Bank B has only one loan of $$$$44\mathrm{.}0$ million$$ outstanding, which it also expects will be repaid today. It also has a $10\%$ probability of not being repaid.$$ Calculate:

a$.$ The expected payoff of Bank A$.$

b$.$ The expected payoff of Bank B$.$

c$.$ The standard deviation of the overall payoff of Bank A$.$

d$.$ The standard deviation of the overall payoff of Bank B$.$