A discrete random variable X has the probability mass function (pmf) given by:
P[X = -1] = 1/2
P[X = 1] = 1/4
P[X = 0] = 1/8
P[X = 5] = 1/16
If Y = sin(rX), find the pmf for Y.
P[X = x] = 0.2, for x = -1, 0, 1, 2.
If Y = X - X, find the pmf of Y, P(Y = y), and then E[Y].