For the probability density function, over the given interval, find E(x), E(x²), the mean, the variance, and the standard deviation. 30 ƒ(x) = f (430 x) dx -x|d, [0, 30]
For the probability density function, over the given interval, find E(x), E(x²), the mean, the variance, and the standard deviation. 30 ƒ(x) = f (430 x) dx -x|d, [0, 30]
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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![**Problem Statement:**
For the probability density function, over the given interval, find \( E(x) \), \( E(x^2) \), the mean, the variance, and the standard deviation.
**Function Definition:**
\[
f(x) = \int_{0}^{30} \left( \frac{1}{450} x \right) \, dx
\]
**Interval:**
\[ [0, 30] \]
**Explanation:**
The task involves solving the integral of the given probability density function over the interval \([0, 30]\). You need to compute the expected value \( E(x) \), the expected value of the square \( E(x^2) \), and subsequently determine the mean. With these results, you can calculate the variance and standard deviation of the distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F939f19e0-6626-477a-ba7a-4282434e880a%2F37453464-fd1b-41b8-99bc-6a92260c449c%2Fwlz5wa8_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
For the probability density function, over the given interval, find \( E(x) \), \( E(x^2) \), the mean, the variance, and the standard deviation.
**Function Definition:**
\[
f(x) = \int_{0}^{30} \left( \frac{1}{450} x \right) \, dx
\]
**Interval:**
\[ [0, 30] \]
**Explanation:**
The task involves solving the integral of the given probability density function over the interval \([0, 30]\). You need to compute the expected value \( E(x) \), the expected value of the square \( E(x^2) \), and subsequently determine the mean. With these results, you can calculate the variance and standard deviation of the distribution.
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