Question 1 Consider two random variables X, Y (not necessarily independent), and two (a) real numbers a and b. Prove that Var(aX+bY) = a² Var(X)+b² Var(Y)+2ab Cov(X, Y). (Hint: Use the properties of...

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Extracted text: Question 1 Consider two random variables X, Y (not necessarily independent), and two (a) real numbers a and b. Prove that Var(aX+bY) = a² Var(X)+b² Var(Y)+2ab Cov(X, Y). (Hint: Use the properties of Cov() reviewed in class.) Prove that E[{X - E(X)}²] = E(X²) – {E(X)}², i.e., the two expressions (b) for Var(X) are indeed equivalent. Prove that E[{X – E(X | Y)}² | Y] = E(X² | Y) – {E(X | Y)}², i.e., the two expressions for Var(X | Y) are indeed equivalent.