Question: 1. Let X be a discrete random variable whose PMF is 20 2(1 -0) 1 - 6 P(O) = P(1) = 2 P(2) = P(3)

1. Let X be a discrete random variable whose PMF is 20 2(1 -0) 1 - 6 P(O) = P(1) = 2 P(2) = P(3) = 3 3 Suppose that X1, ..., Xn are iid samples of X (n > 0). (a) Find the MME for 0. [10 marks] (b) Is the MME unbiased? Is it asymptotically unbiased? [10 marks] (c) Find the MLE for 0. [10 marks] (d) Is the MLE unbiased? Is it asymptotically unbiased? [10 marks]

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