An insurance policy for water damage pays an amount of damage up to $450. The amount of damage is uniformly distributed between $250 and $1,250. The amount of damage exceeding $450 is covered by a...

An insurance policy for water damage pays an amount of damage up to $450. The amount of damage is uniformly distributed between $250 and $1,250. The amount of damage exceeding $450 is covered by a supplement policy up to $500. Let the random variable Y be the amount of damage paid by the supplement policy. What are the expected value and the probability distribution function of Y?