C2. A random variable X is said to follow the discrete uniform distribution on {1,2,.. , n} if each value x in that set {1, 2, ..., n} is equally likely. n +1 (a) Show that the expectation of X is EX = 2 (b) Find the variance of X. (c) Let Y be a discrete uniform distribution on {a, a + 1, a + 2,...,b – 1,6}, for integers a and b with a < b. Using parts (a) and (b), but without calculating any sums directly, find the expectation and variance of Y.

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