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We have the following information about the independent random variables X and Y: of = 5.4 and o= 7.7. Calculate the variance of Z = 5X - 4Y. 0²/2 =

We have the following information about the independent random variables X and Y: of = 5.4 and o= 7.7. Calculate the variance of Z = 5X - 4Y. 0²/2 =

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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We have the following information about the independent random variables \(X\) and \(Y\): \[ \sigma_X^2 = 5.4 \quad \text{and} \quad \sigma_Y^2 = 7.7. \] Calculate the variance of \(Z = 5X - 4Y\). \[ \sigma_Z^2 = \] To calculate the variance \(\sigma_Z^2\) of the random variable \(Z = 5X - 4Y\), use the formula for the variance of a linear combination of independent random variables: \[ \sigma_Z^2 = (5^2) \sigma_X^2 + (-4)^2 \sigma_Y^2. \] Given \(\sigma_X^2 = 5.4\) and \(\sigma_Y^2 = 7.7\), substitute these values into the formula: \[ \sigma_Z^2 = 25 \times 5.4 + 16 \times 7.7. \]
Transcribed Image Text:We have the following information about the independent random variables \(X\) and \(Y\): \[ \sigma_X^2 = 5.4 \quad \text{and} \quad \sigma_Y^2 = 7.7. \] Calculate the variance of \(Z = 5X - 4Y\). \[ \sigma_Z^2 = \] To calculate the variance \(\sigma_Z^2\) of the random variable \(Z = 5X - 4Y\), use the formula for the variance of a linear combination of independent random variables: \[ \sigma_Z^2 = (5^2) \sigma_X^2 + (-4)^2 \sigma_Y^2. \] Given \(\sigma_X^2 = 5.4\) and \(\sigma_Y^2 = 7.7\), substitute these values into the formula: \[ \sigma_Z^2 = 25 \times 5.4 + 16 \times 7.7. \]
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