Let X be the total medical expenses in 1000s of dollars incurred by a particular individual during a given year Although X is a discrete random variable suppose its distribution is quite well approximated by a continuous distribution with pdf f x k 1 x 2 5 7 for x 0 a What is the value of k b Graph the pdf of X c What are the expected value and standard deviation of total medical expenses d This individual is covered by an insurance plan that entails a 500 deductible provision so the first 500 worth of expenses are paid by the individual Then the plan will pay 80 of any additional expenses exceeding 500 and the maximum payment by the individual including the deductible amount is 2500 Let Y denote the amount of this individual s medical expenses paid by the insurance company What is the expected value of Y Hint First figure out what value of X corresponds to the maximum out of pocket expense of 2500 Then write an expression for Y as a function of X which involves several different pieces and calculate the expected value of this function