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 approxima continuous distribution with pdf f(x) = k1+ -4 for x 2 0. (a) what is the value of k? (b) Graph the pdf of X. f(x) f(x) f(x) 1.애 1.아 1.아 0.8 0.8 0.8 0.6 0.6 0.6 0.4 04 0.4 0.2 0.2 0.2
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 approxima continuous distribution with pdf f(x) = k1+ -4 for x 2 0. (a) what is the value of k? (b) Graph the pdf of X. f(x) f(x) f(x) 1.애 1.아 1.아 0.8 0.8 0.8 0.6 0.6 0.6 0.4 04 0.4 0.2 0.2 0.2
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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) = k1- for x 2 o.
(a) What is the value of k?
(b) Graph the pdf of X.
f(x)
f(x)
f(x)
1.0
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
4
6.
2
f(x)
1.0
0.8
0.6
0.4
0.2
8.
(c) What is the expected value of total medical expenses? (Round your answer to the nearest cent.)
What is the standard deviation of total medical expenses? (Round your answer to the nearest cent.)
(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.] (Round your answer to the nearest cent.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d158991-3671-4459-aef6-bd0615668acc%2F34c915aa-ee3f-4049-93ba-213b94336d41%2Frc8smxq_processed.png&w=3840&q=75)
Transcribed Image Text: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) = k1- for x 2 o.
(a) What is the value of k?
(b) Graph the pdf of X.
f(x)
f(x)
f(x)
1.0
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
4
6.
2
f(x)
1.0
0.8
0.6
0.4
0.2
8.
(c) What is the expected value of total medical expenses? (Round your answer to the nearest cent.)
What is the standard deviation of total medical expenses? (Round your answer to the nearest cent.)
(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.] (Round your answer to the nearest cent.)
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