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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
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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7) Please provide a correct answer with a full method explanation and do not copy and paste from other similar questions.

### 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.
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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