The table below shows the probability distribution of the random variable X. a. Find the mean of the random variable. b. Obtain the standard deviation o of the random variable. X 1 2 3 P(X=x) 0.2 0.1 0.7 a. Find the mean of the random variable. μ= 2.5 (Round to two decimal places as needed.) b. Obtain the standard deviation of the random variable. Question Viewer σ= (Round to two dccimar places as needed.)
The table below shows the probability distribution of the random variable X. a. Find the mean of the random variable. b. Obtain the standard deviation o of the random variable. X 1 2 3 P(X=x) 0.2 0.1 0.7 a. Find the mean of the random variable. μ= 2.5 (Round to two decimal places as needed.) b. Obtain the standard deviation of the random variable. Question Viewer σ= (Round to two dccimar places as needed.)
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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Answer b
![**Understanding Probability Distributions**
The table below shows the probability distribution of the random variable \(X\).
| \(x\) | 1 | 2 | 3 |
|----------------|-----|-----|-----|
| \(P(X = x)\) | 0.2 | 0.1 | 0.7 |
**Questions:**
**a. Find the mean of the random variable.**
The mean \( \mu \) is calculated as follows:
\[ \mu = 2.5 \]
(Round to two decimal places as needed.)
**b. Obtain the standard deviation \( \sigma \) of the random variable.**
\[ \sigma = \]
(Round to two decimal places as needed.)
In the graph:
- The variable \( x \) can take on the values \( 1, 2, \) or \( 3 \).
- The corresponding probabilities of these values are \( 0.2, 0.1, \) and \( 0.7 \), respectively.
To further understand the visual representation:
- Along the horizontal axis, the values 1, 2, and 3 are marked.
- On the vertical axis, the probabilities \( P(X = x) \) are represented.
This table and its subsequent calculations help in understanding the central tendency (mean) and dispersion (standard deviation) of the given random variable \( X \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02ebb731-29eb-4cd6-ba2a-cc2ff28bf3c8%2F83444201-ad0f-4f00-9ed5-779d88d75bc1%2F4owakus_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Probability Distributions**
The table below shows the probability distribution of the random variable \(X\).
| \(x\) | 1 | 2 | 3 |
|----------------|-----|-----|-----|
| \(P(X = x)\) | 0.2 | 0.1 | 0.7 |
**Questions:**
**a. Find the mean of the random variable.**
The mean \( \mu \) is calculated as follows:
\[ \mu = 2.5 \]
(Round to two decimal places as needed.)
**b. Obtain the standard deviation \( \sigma \) of the random variable.**
\[ \sigma = \]
(Round to two decimal places as needed.)
In the graph:
- The variable \( x \) can take on the values \( 1, 2, \) or \( 3 \).
- The corresponding probabilities of these values are \( 0.2, 0.1, \) and \( 0.7 \), respectively.
To further understand the visual representation:
- Along the horizontal axis, the values 1, 2, and 3 are marked.
- On the vertical axis, the probabilities \( P(X = x) \) are represented.
This table and its subsequent calculations help in understanding the central tendency (mean) and dispersion (standard deviation) of the given random variable \( X \).
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