In Example 7.30, we started with U = I(X₁ = 0) and used a conditional expectation argument to obtain an unbiased estimator of the zero-defect probability based on the sufficient statistic. Consider now sPtarting with a different statistic:

Show that the improved estimator based on the sufficient statistic is identical to the one obtained in the cited example. Show that the improved estimator based on the sufficient statistic is identical to the one obtained in the cited example.

Example 7.30

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U = I(X₂ = 0)/n.