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Practice Question 2: Let X₁ a random variable with expected value (mean) E(X)= 17 and variance V(X₁)= 12. Let X; 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 = 9X; + 10x₂. a. What is the expected value of the random variable Y, E(Y)? b. What is the variance of the random variable Y, V(Y)? c. What is the correlation between X₁ and X₂, Corr(X₁,X 2)?

Practice Question 2: Let X₁ a random variable with expected value (mean) E(X)= 17 and variance V(X₁)= 12. Let X; 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 = 9X; + 10x₂. a. What is the expected value of the random variable Y, E(Y)? b. What is the variance of the random variable Y, V(Y)? c. What is the correlation between X₁ and X₂, Corr(X₁,X 2)?

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. What is the expected value of the random variable Y, E(Y)? b. What is the variance of the random variable Y, V(Y)? c. What is the correlation between X₁ and X₂, Corr(X₁,X 2)? 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.
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. What is the expected value of the random variable Y, E(Y)? b. What is the variance of the random variable Y, V(Y)? c. What is the correlation between X₁ and X₂, Corr(X₁,X 2)? 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.
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