It is given that:
We toss two dice with sample space Ω = {(i, j), 1 ≤ i, j ≤ 6} and the σ-algebra is generated by the events Ak = {(i,j) : max(i,j) = k} (k = 1, . . . , 6). Show that whereas X1(i, j) = max(i, j) is a random variable in the corresponding probability space, X2(i, j) = i + j is...