Consider two independent Bernoulli r.v., U and V, both with probability of success 1/2. Let X=U+V and Y=∣U−V∣. (a) Calculate the covariance of X and Y,σ X,Y.
(b)Are X and Y independent? Justify your answer. (c) Find the random variable expressed as the conditional expectation of Y given X, i.e., E[Y∣X]. If it has a "named" distribution, you must state it. Otherwise support and pdf is enough.