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Let X₁ a random variable with expected value (mean) E(X₁)= 17 and variance V(X₁) = 12. Let X₂ another random variable with expected value (mean) E(X₂) = 22 and variance V(X₂) = 16. The covariance between X₁ and X₂ is Cov(X1,X 2)=9. Let a new random variable Y defined as Y = 9X₁ + 10x₂. a. d. Explain briefly the meaning of the correlation of these two random variables X₁ and X2. e. Explain briefly if X₁ and X₂ are linearly independent or not.

Let X₁ a random variable with expected value (mean) E(X₁)= 17 and variance V(X₁) = 12. Let X₂ another random variable with expected value (mean) E(X₂) = 22 and variance V(X₂) = 16. The covariance between X₁ and X₂ is Cov(X1,X 2)=9. Let a new random variable Y defined as Y = 9X₁ + 10x₂. a. d. Explain briefly the meaning of the correlation of these two random variables X₁ and X2. e. Explain briefly if X₁ and X₂ are linearly independent or not.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Practice Question 2: Let X₁ a random variable with expected value (mean) E(X₁) = 17 and variance V(X₁) = 12. Let X₂ another random variable with expected value (mean) E(X₂) = 22 and variance V(X₂) = 16. The covariance between X₁ and X₂ is Cov(X1,X 2)=9. Let a new random variable Y defined as Y = 9X₁ + 10x₂. a. d. Explain briefly the meaning of the correlation of these two random variables X₁ and X2. e. Explain briefly if X₁ and X₂ are linearly independent not.
Transcribed Image Text:Practice Question 2: Let X₁ a random variable with expected value (mean) E(X₁) = 17 and variance V(X₁) = 12. Let X₂ another random variable with expected value (mean) E(X₂) = 22 and variance V(X₂) = 16. The covariance between X₁ and X₂ is Cov(X1,X 2)=9. Let a new random variable Y defined as Y = 9X₁ + 10x₂. a. d. Explain briefly the meaning of the correlation of these two random variables X₁ and X2. e. Explain briefly if X₁ and X₂ are linearly independent not.
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