please please help me out for these question below. They are very important to me. As I am not good on Statistic and I don't have the model answers for them, I really want someone who can show me the answers about them. Therefore, I can check if i was doing the questions in the right way.
Thank you very much!!!
Question 1 -- Let X, Y and Z be random variables.
(a) Define the covariance Cov(X, Y ).
(b) Prove that Cov(Z,X + Y ) = Cov(Z,X) + Cov(Z, Y ).
(c) Suppose that X and Y are independent, with Var(X) = 25 and Var(Y ) = 6,
and that Z = X + 2Y . Find the correlation between X and Z.