Two fair and independent dice (each with six faces) are thrown. Let X1 be the score on the first die and X2 the score on the second. Let X = X1 + X2 , Y = X1 X2 and Z = M in(X1; X2) .
(i) Compute: V ar(X); V ar(Y ); V ar(Z); Cov(X; Y ); Cov(Y; Z) and Cov(Z; X).
(ii) Are the two random variables X and Y independent?
(iii) Are the two random variables Y and Z independent?
(iv) Are the two random variables Z and X independent?