Suppose that you hold a piece of land in the City of London that you may want to sell in one year. As a U$.$S$.$ resident, you are concerned with the dollar value of the land. Assume that, if the British economy booms in the future, the land will be worth $2,807$ and one British pound will be worth $$1\mathrm{.}45.$ If the British economy slows down, on the other hand, the land will be worth less, i$.$e$.,1,570,$ but the pound will be stronger, i$.$e$.,$ $$1\mathrm{.}46/.$ You feel that the British economy will experience a boom with a $60\%$ probability and a slow$-$down with a $40\%$ probability.

$($a$)$ Estimate your exposure b to the exchange risk.