Let X as well as U denote random variables, and suppose that E[U|X] = 1 and that E[X] = 2.
a) What is E[U]? Provide a proof for your answer.
b) What is E [XU]? Provide a proof for your answer
c) What is Cov [X,U]? Provide a proof for your answer
d) Is U mean independent of X? Explain briefly
e) Is U uncorrected with X? Explain briefly
f) Do you have enough info. to determine whether X is independent of U? Explain briefly.