Suppose you are a British venture capitalist holding a major stake in an e$-$commerce start$-$up in Silicon Valley. As a British resident, you are concerned with the pound value of your U$.$S$.$ equity position. Assume that if the American economy booms in the future, your equity stake will be worth $$1,001,980,$ and the exchange rate will be $$1\mathrm{.}4/.$ If the American economy experiences a recession, on the other hand, your American equity stake will be worth $$502,240,$ and the exchange rate will be $$1\mathrm{.}6/.$ You assess that the American economy will experience a boom with a $50$ percent probability and a recession with a $50$ percent probability.

a$.$ Estimate your exposure to the exchange risk. $($Round final answer to nearest dollar.$)$

b$.$ Compute the variance of the pound value of your American equity position that is attributable to the exchange rate uncertainty. $($Round final answer to nearest dollar.$)$