7.12 Let X1,..., Xn be a random sample from a population with pmf Po(X = x) = 0* (1 – 0)'-, x=0 or 1, 0<0< || (a) Find the method of moments estimator and MLE of 0. (b) Find the mean squared errors of each of the estimators. (c) Which estimator is preferred? Justify your choice.

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7.12 Let X1,..., Xn be a random sample from a population with pmf
Po(X = x) = 0" (1 – 0)!-², x= 0 or 1, 0<0<;.
(a) Find the method of moments estimator and MLE of 0.
(b) Find the mean squared errors of each of the estimators.
(c) Which estimator is preferred? Justify your choice.
Transcribed Image Text:7.12 Let X1,..., Xn be a random sample from a population with pmf Po(X = x) = 0" (1 – 0)!-², x= 0 or 1, 0<0<;. (a) Find the method of moments estimator and MLE of 0. (b) Find the mean squared errors of each of the estimators. (c) Which estimator is preferred? Justify your choice.
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