The amount of snow damage in a certain region is uniformly distributed between $250 and $1250. A basic insurance policy for snow damage pays an amount of damage up to $450. The amount of damage exceeding $450 is covered by a supplemental policy up to $500. Let Y be a random variable representing the amount paid by the supplemental policy. In the followings provide complete derivations and explanation of results. a) What is the probability that the supplemental policy will have to be used? b) What is the average of the amount paid by the supplemental policy Y ? c) What is the CDF of Y ? d) Draw the CDF of Y, with clear indication of all the defining numerical points