The random variables Y1 and Y2 are such that E(Y1) = 4, E(Y2) = 1, V(Y1) = 2 and V(Y2) =
Chapter 5, Problem 5.97(choose chapter or problem)
The random variables Y1 and Y2 are such that E(Y1) = 4, E(Y2) = 1, V(Y1) = 2 and V(Y2) = 8. a What is Cov(Y1, Y1)? b Assuming that the means and variances are correct, as given, is it possible that Cov(Y1, Y2) = 7? [Hint: If Cov(Y1, Y2) = 7, what is the value of , the coefficient of correlation?] c Assuming that the means and variances are correct, what is the largest possible value for Cov(Y1, Y2)? If Cov(Y1, Y2) achieves this largest value, what does that imply about the relationship between Y1 and Y2?d Assuming that the means and variances are correct, what is the smallest possible value for Cov(Y1, Y2)? If Cov(Y1, Y2) achieves this smallest value, what does that imply about the relationship between Y1 and Y2?
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