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Let X₁, ..., X_n be i.i.d. random variables having the normal distribution N(θ, 1), where θ = 0 or 1. Consider the estimation of θ.

(a) Let be the class of nonrandomized rules (estimators), i.e., estimators that take values 0 and 1 only. Show that there does not exist any unbiased estimator of θ in ℑ.

(b) Find an estimator in that is approximately unbiased.

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