The proportion of time X that an industrial robot is in operation during a 40-hour work week is a random variable with probability density function 2x 0
The proportion of time X that an industrial robot is in operation during a 40-hour work week is a random variable with probability density function 2x 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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Question
The proportion of time X that an industrial robot is in operation during a 40hour work-week is a random variable with probability density
Note: The probability density function is shown in img3.jpg
a) Find E(X) and V(X)
b) For the robot understudy, the profit Y for a week is given by
Y = 200X -60
c) Find an interval in which the profit should lie for at least 75% of the weeks that the robot is in use. [Hint: Use Tchebysheff's theorem.]
![**Problem Statement:**
The proportion of time \( X \) that an industrial robot is in operation during a 40-hour work week is a random variable with probability density function
\[
f(x) =
\begin{cases}
2x & 0 \le x \le 1 \\
0 & \text{elsewhere}
\end{cases}
\]
**Questions:**
a. Find \( E(X) \) and \( V(X) \).
b. For the robot under study, the profit \( Y \) for a week is given by
\[ Y = 200X - 60 \]
Find \( E(Y) \) and \( V(Y) \).
c. Find an interval in which the profit should lie for at least 75% of the weeks that the robot is in use. [Hint: Use Tchebysheff’s theorem.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07ecadc9-0017-4589-b85c-6c95e82cc0ef%2F675a8989-0749-4469-beb1-703b1a296857%2Fnawlqfe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The proportion of time \( X \) that an industrial robot is in operation during a 40-hour work week is a random variable with probability density function
\[
f(x) =
\begin{cases}
2x & 0 \le x \le 1 \\
0 & \text{elsewhere}
\end{cases}
\]
**Questions:**
a. Find \( E(X) \) and \( V(X) \).
b. For the robot under study, the profit \( Y \) for a week is given by
\[ Y = 200X - 60 \]
Find \( E(Y) \) and \( V(Y) \).
c. Find an interval in which the profit should lie for at least 75% of the weeks that the robot is in use. [Hint: Use Tchebysheff’s theorem.]
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