Let X1, , Xn be a random sample from a population with pmf P(X x) x (1 )1 x, x 0 or 1, 0 1 2 a Find the method of moments estimator and MLE of b Find the mean squared errors of each of the estimators c Which estimator is preferred Justify your choice

Question: Let X1,..., Xn be a random sample from a population with pmf P(X = x) = x (1 - )1-x, x = 0 or 1,

Let X1,..., Xn be a random sample from a population with pmf
Pθ(X = x) = θx (1 - θ)1-x, x = 0 or 1, 0 ≤ θ ≤ 1/2.
a. Find the method of moments estimator and MLE of θ.
b. Find the mean squared errors of each of the estimators.
c. Which estimator is preferred? Justify your choice.

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