2. (i) Suppose a random variable X has only two possible outcomes, a and b, with probabilities p and q respectively (p + q = 1). Find the expected value (or the mean) of X, and show that the standard deviation is vpqlb -al. (ii) If p = q = , show that every outcome is exactly one standard devia- tion from the mean. If you want, you can assume without loss of generality that b > a