The proportion of people who respond to a certain mail-order solicitation is a random variable X having the following density function. f(x) = 2(x+3) 7 O " 0
The proportion of people who respond to a certain mail-order solicitation is a random variable X having the following density function. f(x) = 2(x+3) 7 O " 0
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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![The proportion of people who respond to a certain mail-order solicitation is a random variable \( X \) having the following density function.
\[
f(x) =
\begin{cases}
\frac{2(x+3)}{7}, & 0 < x < 1, \\
0, & \text{elsewhere}
\end{cases}
\]
Find the variance of \( X \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe7e575d-dfd7-411c-ad5f-62e2be64ba9f%2Febafce7f-618a-4e36-b54c-86decbcecdbf%2Foxqwoy5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The proportion of people who respond to a certain mail-order solicitation is a random variable \( X \) having the following density function.
\[
f(x) =
\begin{cases}
\frac{2(x+3)}{7}, & 0 < x < 1, \\
0, & \text{elsewhere}
\end{cases}
\]
Find the variance of \( X \).
![**Problem Description:**
If a dealer's profit, in units of $3000, on a new automobile can be looked upon as a random variable \(X\) having the density function below, find the average profit per automobile.
**Density Function:**
\[
f(x) =
\begin{cases}
\frac{1}{12}(7 - x), & 0 < x < 2, \\
0, & \text{elsewhere}
\end{cases}
\]
**Explanation:**
This presents a piecewise probability density function (PDF) \(f(x)\) defined for a random variable \(X\). The function is defined as:
- \(\frac{1}{12}(7 - x)\) for \(0 < x < 2\): This indicates that within the range of 0 to 2, the density function follows a linear decrease as a function of \(x\).
- 0 elsewhere: Outside the range of 0 to 2, the probability density function is zero, meaning there is no chance of the profit value falling outside this interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe7e575d-dfd7-411c-ad5f-62e2be64ba9f%2Febafce7f-618a-4e36-b54c-86decbcecdbf%2Fe2c6gp7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
If a dealer's profit, in units of $3000, on a new automobile can be looked upon as a random variable \(X\) having the density function below, find the average profit per automobile.
**Density Function:**
\[
f(x) =
\begin{cases}
\frac{1}{12}(7 - x), & 0 < x < 2, \\
0, & \text{elsewhere}
\end{cases}
\]
**Explanation:**
This presents a piecewise probability density function (PDF) \(f(x)\) defined for a random variable \(X\). The function is defined as:
- \(\frac{1}{12}(7 - x)\) for \(0 < x < 2\): This indicates that within the range of 0 to 2, the density function follows a linear decrease as a function of \(x\).
- 0 elsewhere: Outside the range of 0 to 2, the probability density function is zero, meaning there is no chance of the profit value falling outside this interval.
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