Determine the mean and variance of the random variable with the following probability mass function. f(x) = (64/21)(1/4)*, x = 1,2,3 Round your answers to three decimal places (e.g. 98.765). Mean = 1.286 Variance = i 1.157
Determine the mean and variance of the random variable with the following probability mass function. f(x) = (64/21)(1/4)*, x = 1,2,3 Round your answers to three decimal places (e.g. 98.765). Mean = 1.286 Variance = i 1.157
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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![### Determine the Mean and Variance of a Random Variable
To calculate the mean and variance of a random variable with a given probability mass function (PMF), follow the steps below:
The given PMF is:
\[ f(x) = \left(\frac{64}{21}\right) \left(\frac{1}{4}\right)^x \]
for \( x = 1, 2, 3 \).
Round your answers to three decimal places (e.g., 98.765).
#### Mean Calculation:
The mean \(\mu\) is given by the formula:
\[ \mu = \sum_{x} x \cdot P(X=x) \]
Based on calculations from the problem, the determined mean is:
\[ \text{Mean} = 1.286 \]
#### Variance Calculation:
The variance \(\sigma^2\) is given by the formula:
\[ \sigma^2 = \sum_{x} (x - \mu)^2 \cdot P(X=x) \]
Based on calculations from the problem, the determined variance is:
\[ \text{Variance} = 1.157 \]
Please note that the values of mean and variance are precise to three decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7824f8d0-65fb-442c-84f7-7ea5547717e1%2Fac10d978-2c01-464d-a354-1c2fd0b9278c%2Fykvleuu_processed.png&w=3840&q=75)
Transcribed Image Text:### Determine the Mean and Variance of a Random Variable
To calculate the mean and variance of a random variable with a given probability mass function (PMF), follow the steps below:
The given PMF is:
\[ f(x) = \left(\frac{64}{21}\right) \left(\frac{1}{4}\right)^x \]
for \( x = 1, 2, 3 \).
Round your answers to three decimal places (e.g., 98.765).
#### Mean Calculation:
The mean \(\mu\) is given by the formula:
\[ \mu = \sum_{x} x \cdot P(X=x) \]
Based on calculations from the problem, the determined mean is:
\[ \text{Mean} = 1.286 \]
#### Variance Calculation:
The variance \(\sigma^2\) is given by the formula:
\[ \sigma^2 = \sum_{x} (x - \mu)^2 \cdot P(X=x) \]
Based on calculations from the problem, the determined variance is:
\[ \text{Variance} = 1.157 \]
Please note that the values of mean and variance are precise to three decimal places.
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