Let X₁ a random variable with expected value (mean) E(X) = 17 and variance V(X) = 12. Let Xz 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 = 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 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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