Suppose that the length X of the life (in years) of a battery for a computer has a distribution that can be described by the pdf: 2 f(x) = 49 Determine the probability that the battery fails before the one year warranty expires on the computer.
Suppose that the length X of the life (in years) of a battery for a computer has a distribution that can be described by the pdf: 2 f(x) = 49 Determine the probability that the battery fails before the one year warranty expires on the computer.
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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![**Problem Statement:**
Suppose that the length X of the life (in years) of a battery for a computer has a distribution that can be described by the probability density function (pdf):
\[
f(x) = \frac{x}{49} e^{-\frac{x^2}{98}}
\]
Determine the probability that the battery fails before the one-year warranty expires on the computer.
**Explanation of the Function:**
The function \( f(x) \) is a probability density function that models the distribution of battery life. Here:
- \( x \) represents the years of battery life.
- The coefficient \( \frac{x}{49} \) is a scaling factor for the probability.
- \( e^{-\frac{x^2}{98}} \) is the exponential part of the function, where \( e \) is Euler's number.
To solve this problem, you would integrate the function from 0 to 1 to find the probability that the battery fails within the first year.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff490fc5e-f29e-4ef4-a7f0-8835aa77e897%2Fca0d9905-6141-4c52-aaef-a6ee4bf757c3%2Fhdunp39_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Suppose that the length X of the life (in years) of a battery for a computer has a distribution that can be described by the probability density function (pdf):
\[
f(x) = \frac{x}{49} e^{-\frac{x^2}{98}}
\]
Determine the probability that the battery fails before the one-year warranty expires on the computer.
**Explanation of the Function:**
The function \( f(x) \) is a probability density function that models the distribution of battery life. Here:
- \( x \) represents the years of battery life.
- The coefficient \( \frac{x}{49} \) is a scaling factor for the probability.
- \( e^{-\frac{x^2}{98}} \) is the exponential part of the function, where \( e \) is Euler's number.
To solve this problem, you would integrate the function from 0 to 1 to find the probability that the battery fails within the first year.
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