Carlos and Michael eachflip a fair coin twice. Let

X= "the number of heads obtained by Carlos" - "the number of heads obtained by Michael",

Y = "the number of heads obtained by Carlos" + "the number of heads obtained by Michael".

(a) Find the probabilities for all values of (X; Y ).

(b) Find P[X + Y = 1] and P[X + Y = 2].

(c) Find and sketch pX;Y (x; y) and pX(x).

(d) Find the correlation and covariance, and indicate whether the random variables are

independent, orthogonal,or uncorrelated.