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We have the following information about the random variables X and Y: μx= 4 `, My = 5 Cov(X, Y) = στ 8 15 4 225 ● of = 2 75 of = 11 225 Calculate the standard deviation of Z = 3Y – X.

We have the following information about the random variables X and Y: μx= 4 `, My = 5 Cov(X, Y) = στ 8 15 4 225 ● of = 2 75 of = 11 225 Calculate the standard deviation of Z = 3Y – X.

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 random variables \( X \) and \( Y \): \[ \mu_X = \frac{4}{5}, \quad \mu_Y = \frac{8}{15}, \quad \sigma_X^2 = \frac{2}{75}, \quad \sigma_Y^2 = \frac{11}{225}, \] \[ Cov(X,Y) = \frac{4}{225}. \] Calculate the standard deviation of \( Z = 3Y - X \). \[ \sigma_Z = \boxed{} \]
Transcribed Image Text:We have the following information about the random variables \( X \) and \( Y \): \[ \mu_X = \frac{4}{5}, \quad \mu_Y = \frac{8}{15}, \quad \sigma_X^2 = \frac{2}{75}, \quad \sigma_Y^2 = \frac{11}{225}, \] \[ Cov(X,Y) = \frac{4}{225}. \] Calculate the standard deviation of \( Z = 3Y - X \). \[ \sigma_Z = \boxed{} \]
Expert Solution
Step 1: Determine the given data

From the provided information,

sigma squared subscript X equals 2 over 75 sigma squared subscript Y equals 11 over 225 C o v open parentheses X comma Y close parentheses equals 4 over 225

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