Answered: Let X be the total medical expenses (in…

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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Question

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

What is the value of k?

What is the expected value of total medical expenses?

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?

The equation displayed is:

\[ f(x) = k \left( 1 + \frac{x}{2.5} \right)^{-5} \]

This function is defined for $ x \geq 0 $.

### Explanation:

- **Function Notation**: $ f(x) $ represents a function of $ x $.
- **Constant**: $ k $ is a constant that scales the function.
- **Expression Inside Parentheses**: $ \left( 1 + \frac{x}{2.5} \right) $ represents a transformation of the variable $ x $ where it is first divided by 2.5 and then increased by 1.
- **Exponent**: The expression is raised to the power of -5, indicating an inverse effect and compression.
- **Domain**: The function is defined for all $ x $ values greater than or equal to 0.

This function could be used in various applications, such as modeling decay processes or other scenarios where an inverse relationship is involved.

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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