#1. Recall the family of distributions with pmf pX(x; p) = p if x = −1...

#1. Recall the family of distributions with pmf pX(x; p) = p if x = −1 2p if x = 0 (1 − 3p) if x = 1 . Here p is an unknown parameter, and 0 ≤ p ≤ 1/3. Let X1, X2, . . . , Xn be iid with common pmf a member of this family. (i) Find the MOM estimator of p. (ii) Find the MLE estimator of p. (Hint: The statistics A, B, C from assignment #3 will be useful.) (iii) A sample from this distribution produced the values { 1, 1, 1, -1, 0, 0, 1, -1, 1, 1, -1, 1, 1, -1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, -1, 1, 1, 1, -1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, -1, 0, -1, 1, 1, 0, 0 } (There are 8 -1’s, 15 0’s and 27 1’s.) What are the MOM and MLE estimates of p for this data set? Which seems to fit the data better? Explain your answer.

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orchestra answered 1 year ago

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