Exercise 6. Suppose a random variable has support: {0, 1, 2,4} and its pmf is: X 0 1 2 4 f(x) 3/7 2/7 1/7 1/7 (a) Calculate an explicit expression for the moment generating function: M(t). (b) Using your moment generating function, calculate E(X²) and E(X), and thereby the variance 0².

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