forLet 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 + 2².5)¯x ≥ 0.(a) What is the value of k?1.2(b) Graph the pdf of X.f(x)f(x)f(x)f(x)1.00.80.60.40.22468X4224666248O(c) What is the expected value of total medical expenses? (Round your answer to the nearest cent.)$ 6.25xWhat is the standard deviation of total medical expenses? (Round your answer to the nearest cent.)$ 6.25x(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 theindividual (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-pocketexpense 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.] (Round your answer to the nearest cent.)$1.00.80.60.40.28X1.00.80.60.40.2XO1.00.80.60.40.2

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 its distribution is quite well approximated by a continuous distribution with pdf f(x) = (1+) for x 20. (a) What is the value of K?