1. A manager of a certain office is offered a bonus each month if the total expenses are under 1000. The bonus is half the difference between 1000 and the expenses. So, for example, if expenses were 800, the bonus would be 100. Find the expected value of the bonus in each of the following cases.
(a) Expenses are exponentially distributed with a mean of 2000.
(b) Expenses are uniformly distributed on the interval [0, 4000].