Question: LetY1andY2be two random variables that satisfy:E(Y1) = 4,E(Y2) =1,V(Y1) = 2, andV(Y2) = 8. (a) What is Cov(Y1, Y1)? (b) Is it possible that Cov(Y1,Y2)

LetY1andY2be two random variables that satisfy:E(Y1) = 4,E(Y2) =1,V(Y1) = 2, andV(Y2) = 8.

(a) What is Cov(Y1, Y1)?

(b) Is it possible that Cov(Y1,Y2) = 7? [Hint: Suppose that Cov(Y1,Y2) = 7, then what would be the the value of, the coefficient of correlation?] Carefully explain your reasoning.

(c) What is the largest possible value of Cov(Y1, Y2)? If Cov(Y1, Y2) achieves this largest value, what does that imply about the relationship betweenY1andY2? Carefully explain your reasoning.

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