The probability density of a random variable X is given in the figure below 1 From this density, the probability that X is between 0.36 and 1.82 is:
The probability density of a random variable X is given in the figure below 1 From this density, the probability that X is between 0.36 and 1.82 is:
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
![**Title: Understanding Probability Density Functions**
The probability density of a random variable \( X \) is illustrated in the figure below.
**Diagram Explanation:**
- A rectangle represents the probability density function.
- The base of the rectangle lies on the x-axis between the values 0 and 2.
- The height of the rectangle is not labeled but represents a uniform distribution over the interval [0, 2].
From this density, we are asked to calculate the probability that \( X \) is between 0.36 and 1.82.
---
For educational purposes, note that the area under the probability density function curve over a specific interval represents the probability that the random variable falls within that interval. Since the distribution is uniform, you can calculate this probability by finding the area of the rectangle between 0.36 and 1.82. Use the formula:
\[
\text{Probability} = \frac{\text{Length of interval}}{\text{Total length of distribution domain}}
\]
This specific exercise guides a student through understanding how the uniform probability is distributed across the defined interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0645be48-2a82-494d-ae06-198a7d9d9703%2Fd88f8d98-2539-4368-a830-1eb4bce15d09%2Fogn5rzm_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Probability Density Functions**
The probability density of a random variable \( X \) is illustrated in the figure below.
**Diagram Explanation:**
- A rectangle represents the probability density function.
- The base of the rectangle lies on the x-axis between the values 0 and 2.
- The height of the rectangle is not labeled but represents a uniform distribution over the interval [0, 2].
From this density, we are asked to calculate the probability that \( X \) is between 0.36 and 1.82.
---
For educational purposes, note that the area under the probability density function curve over a specific interval represents the probability that the random variable falls within that interval. Since the distribution is uniform, you can calculate this probability by finding the area of the rectangle between 0.36 and 1.82. Use the formula:
\[
\text{Probability} = \frac{\text{Length of interval}}{\text{Total length of distribution domain}}
\]
This specific exercise guides a student through understanding how the uniform probability is distributed across the defined interval.
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