Suppose that X1, ..., Xn is a simple random sample from a discrete distribution with probability mass function, P(X = 0) = 2/3θ, P(X = 1) = 1/3θ, P(X = 2) = 2/3(1 - θ), P(X = 3) = 1/3(1 - θ) where 0 ≤ θ ≤ 1 is the unknown parameter. (a) Derive the method of moments estimator (MME) θ̃ of θ. (b) Determine the MSE (Mean Squared Error) of θ̃. See the lecture notes for the definition of MSE and a computational formula. You need to find E(θ̃) and Var(θ̃) to get the MSE using the computational formula. (c) Explain why the exact sampling distribution θ̃ is tedious. Then use Central Limit Theorem to find the approximate sampling distribution of θ̃. Compare the approximate E(θ̃) and Var(θ̃) from this approximation to the exact E(θ̃) and Var(θ̃) in part (b). (d) Suppose 10 independent observations were taken from the given distribution: (0, 0, 2, 1, 3, 2, 1, 0, 2, 1). What is the numerical value of the method of moments estimator? What is the numerical value of the estimated standard deviation of the method of moments estimator?