Let X be the total medical expenses (in 1000s of dollars)incurred by a particular

Chapter 4, Problem 26

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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 itsdistribution is quite well approximated by a continuousdistribution with pdf f(x) 5 k(1 1 x /2.5)27 for x $ 0.a. What is the value of k?b. Graph the pdf of X.c. What are the expected value and standard deviationof total medical expenses?d. This individual is covered by an insurance plan thatentails a $500 deductible provision (so the first $500worth of expenses are paid by the individual). Thenthe plan will pay 80% of any additional expensesexceeding $500, and the maximum payment by theindividual (including the deductible amount) is$2500. Let Y denote the amount of this individualsmedical expenses paid by the insurance company.What is the expected value of Y? [Hint: First figure out what value of X corresponds tothe maximum out-of-pocket expense of $2500. Thenwrite an expression for Y as a function of X (whichinvolves several different pieces)