Suppose the possible values of X are xi the possible
Suppose the possible values of X are xi the possible
Suppose the possible values of X are {xi}, the possible values of Y are {yj}, and the possible values of X + Y are {zk}. Let Ak denote the set of all pairs of indices (i, j) such that xi + yj = zk; that is,
Ak = {(i, j): xi + yj = zk}.
(a) Argue that
(b) Show that
(c) Using the formula from part (b), argue that
(d) Show that
(e) Prove that
E[X + Y] = E[X] + E[Y]