The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with the following pdf 1sxS 2 f(x) otherwise
The weekly demand for propane gas (in 1000s of gallons) from a particular facility is an rv X with the following pdf 1sxS 2 f(x) otherwise
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Using the screenshot, please obtain an expression for the (100p)th percentile.
![The weekly demand for propane gas (in 1000s of gallons) from a particular facility is a random variable \( X \) with the following probability density function (pdf):
\[
f(x) =
\begin{cases}
2 \left( 1 - \frac{1}{x^2} \right) & \text{for } 1 \leq x \leq 2 \\
0 & \text{otherwise}
\end{cases}
\]
- **Explanation**: The function \( f(x) \) specifies how the probability is distributed across the different values of demand (in 1000s of gallons). For values of \( x \) between 1 and 2, the function \( f(x) \) is defined by the formula \( 2 \left( 1 - \frac{1}{x^2} \right) \). For any other value of \( x \), the probability is 0. This distribution shows how likely different levels of demand are within the specified range. The graph of this function would have a curve starting at \( x = 1 \), ending at \( x = 2 \), and be flat (at \( f(x) = 0 \)) outside of this interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77cac1a6-5ad9-4f72-bdd9-21a202e53df4%2F021bbc63-9f11-40db-a23e-f50b57cfa0c2%2F9kl09q_processed.png&w=3840&q=75)
Transcribed Image Text:The weekly demand for propane gas (in 1000s of gallons) from a particular facility is a random variable \( X \) with the following probability density function (pdf):
\[
f(x) =
\begin{cases}
2 \left( 1 - \frac{1}{x^2} \right) & \text{for } 1 \leq x \leq 2 \\
0 & \text{otherwise}
\end{cases}
\]
- **Explanation**: The function \( f(x) \) specifies how the probability is distributed across the different values of demand (in 1000s of gallons). For values of \( x \) between 1 and 2, the function \( f(x) \) is defined by the formula \( 2 \left( 1 - \frac{1}{x^2} \right) \). For any other value of \( x \), the probability is 0. This distribution shows how likely different levels of demand are within the specified range. The graph of this function would have a curve starting at \( x = 1 \), ending at \( x = 2 \), and be flat (at \( f(x) = 0 \)) outside of this interval.
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