A fair die is tossed twice and let X1 and X2 denote the scores obtained for the two tosses, respectively.
a) Calculate E[X1] and show that var(X1)= 35/12
b) Determine and tabulate the probability distribution of Y= |x1-x2| and show that E[Y]=35/18
c) The random variable Z is defined by Z=X1-X2. Comment with reasons(quantities concerned need not be evaluated) if each of the following statements is true or false.
(i) E(Z^2)=E(Y^2)
(ii) var(Z)=var(Y)