The proportion of people who respond to a certain mail-order solicitation is a random variable X having the following density function. 2(x+2) 5 0
The proportion of people who respond to a certain mail-order solicitation is a random variable X having the following density function. 2(x+2) 5 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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![**Variance of a Random Variable with a Given Density Function**
The proportion of people who respond to a certain mail-order solicitation is a random variable \( X \) having the following density function:
\[ f(x) =
\begin{cases}
\frac{2(x + 2)}{5}, & 0 < x < 1, \\
0, & \text{elsewhere}.
\end{cases} \]
Find the variance of \( X \).
---
**Calculation of Variance, \( \sigma^2 \)**
Calculate the variance, \( \sigma^2 \).
\[ \text{The variance is } \boxed{ \quad }. \]
(Type an integer or a simplified fraction in the box.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f7a11c6-35df-4daf-855c-043e8f69fb75%2Fba46324d-928b-40a9-905d-ca8a312b6877%2Fqdblqke_processed.png&w=3840&q=75)
Transcribed Image Text:**Variance of a Random Variable with a Given Density Function**
The proportion of people who respond to a certain mail-order solicitation is a random variable \( X \) having the following density function:
\[ f(x) =
\begin{cases}
\frac{2(x + 2)}{5}, & 0 < x < 1, \\
0, & \text{elsewhere}.
\end{cases} \]
Find the variance of \( X \).
---
**Calculation of Variance, \( \sigma^2 \)**
Calculate the variance, \( \sigma^2 \).
\[ \text{The variance is } \boxed{ \quad }. \]
(Type an integer or a simplified fraction in the box.)
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