Practice Question 2: Let X, a random variable with expected value (mean) E(X)= 17 and variance V(X₁) 12. Let another random variable with expected value (mean) E(X) = 22 and variance V(X₂) = 16. covariance between X₁ and X₂ is Cov(X1.X2)=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 X₁, Corr(X₁,X 2)?

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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(X) = 22 and variance V(X₂) = 16. The
covariance between X₁ and X2 is Cov(X1.X2)=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 X₁, 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(X) = 17 and variance V(X₁) = 12. Let X; another random variable with expected value (mean) E(X) = 22 and variance V(X₂) = 16. The covariance between X₁ and X2 is Cov(X1.X2)=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 X₁, 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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