(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.) 0.8794 (e) Compute E(X) and ay (Round your answers to four decimal places.) E(X) - 11 0.1114 (f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.) 3182
(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.) 0.8794 (e) Compute E(X) and ay (Round your answers to four decimal places.) E(X) - 11 0.1114 (f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.) 3182
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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I need help with d and f
![Let \( X \) denote the amount of space occupied by an article placed in a \(1-ft^3\) packing container. The probability density function (pdf) of \( X \) is defined as follows:
\[
f(x) = \begin{cases}
90x^2(1-x) & 0 < x < 1 \\
0 & \text{otherwise}
\end{cases}
\]
**(a) Graph the pdf:**
- Four graphs are shown to represent \( f(x) \). The correct graph is identified with a checkmark. The plot has \( x \) on the horizontal axis ranging from 0 to 1, and \( f(x) \) on the vertical axis with a peak around \( x = 0.67 \).
**Obtain the cumulative distribution function (cdf) of \( X \):**
\[
F(x) = \begin{cases}
0 & x < 0 \\
x^3(10 - 9x) & 0 \leq x \leq 1 \\
1 & x > 1
\end{cases}
\]
**Graph the cdf:**
- Four graphs are shown to represent \( F(x) \). The correct graph has \( x \) on the horizontal axis ranging from 0 to 1, and \( F(x) \) on the vertical axis ranging from 0 to 1, showing a smooth curve increasing from 0 to 1.
**(b) What is \( P(X \leq 0.55) \) (i.e., \( F(0.55) \))?**
\[ 0.0233 \]
**(c) Using the cdf, what is \( P(0.3 < X \leq 0.55) \)?**
\[ 0.0231 \]
**(d) What is the 75th percentile of the distribution?**
\[ 0.8794 \] (Incorrect value, as indicated by the cross mark)
**(e) Compute \( E(X) \) and \( \sigma_X \):**
\[ E(X) = \frac{9}{11} \]
\[ \sigma_X = 0.1114 \]
**(f) What is the probability that \( X \) is more than 1 standard deviation from its mean value?**
\[ 318](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7e43dbe-ab72-46fa-955b-a8f42ce6613a%2Fa7f76ce4-8e14-48d2-ae84-2a1cf50f45c9%2Fsjhfb22_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( X \) denote the amount of space occupied by an article placed in a \(1-ft^3\) packing container. The probability density function (pdf) of \( X \) is defined as follows:
\[
f(x) = \begin{cases}
90x^2(1-x) & 0 < x < 1 \\
0 & \text{otherwise}
\end{cases}
\]
**(a) Graph the pdf:**
- Four graphs are shown to represent \( f(x) \). The correct graph is identified with a checkmark. The plot has \( x \) on the horizontal axis ranging from 0 to 1, and \( f(x) \) on the vertical axis with a peak around \( x = 0.67 \).
**Obtain the cumulative distribution function (cdf) of \( X \):**
\[
F(x) = \begin{cases}
0 & x < 0 \\
x^3(10 - 9x) & 0 \leq x \leq 1 \\
1 & x > 1
\end{cases}
\]
**Graph the cdf:**
- Four graphs are shown to represent \( F(x) \). The correct graph has \( x \) on the horizontal axis ranging from 0 to 1, and \( F(x) \) on the vertical axis ranging from 0 to 1, showing a smooth curve increasing from 0 to 1.
**(b) What is \( P(X \leq 0.55) \) (i.e., \( F(0.55) \))?**
\[ 0.0233 \]
**(c) Using the cdf, what is \( P(0.3 < X \leq 0.55) \)?**
\[ 0.0231 \]
**(d) What is the 75th percentile of the distribution?**
\[ 0.8794 \] (Incorrect value, as indicated by the cross mark)
**(e) Compute \( E(X) \) and \( \sigma_X \):**
\[ E(X) = \frac{9}{11} \]
\[ \sigma_X = 0.1114 \]
**(f) What is the probability that \( X \) is more than 1 standard deviation from its mean value?**
\[ 318
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