Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential random variable with parameter 1 20 . Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional miles out of it

The treasurer for pittsburgh iron works wishes to use financial futures to hedge her interest rate exposure. she will sell five treasury futures contracts at $139,000 per contract. it is july and the contracts must be closed out in december of this year. long-term interest rates are currently 7.30 percent. if they increase to 9.50 percent, assume the value of the contracts will go down by 20 percent. also if interest rates do increase by 2.2 percent, assume the firm will have additional interest expense on its business loans and other commitments of $149,000. this expense, of course, will be separate from the futures contracts. a. what will be the profit or loss on the futures contract if interest rates increase to 9.50 percent by december when the contract is closed out