i) Show that (X, Y) pair has the same joint distribution as the (Y+Z, Y) pair, where Z is a independent standard normal random variable.
ii) Using i) show that X,Y pair is a two dimensional normal distribution.
iii) Calculate E(X), Var(X), Corr(X,Y).
iv) Find E(Y | X=x).
v) What is the conditional distribution of Y given X=x?
I would really appreciate if you could help me.