(i) On the measurable space ((, A), define the function X as follows:

where A1, A2 ( A. Examine whether or not X is a r.v.
(ii) On the measurable space ((, A) with ( = {a, b, c, d} and A = {(, {a, b}, {c, d}, (}, define the function X as follows: X (a) = X (b) = -1 X (c) = 1, X (d) = 2, Examine whether or not X is a r.v.
(iii) If ( = {-2, -1, 0, 1, 2} and X is defined on (( by X(ω) = ω determine the field induced by X and that induced by X2. Verify that the latter is contained in the former.

On A1, 1 0 on AnA