Counterexample

Is this true?

The Cramér–Rao bound is attained by the UMVUE

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

86 counterexamples are free — including most of the ones Part C leans on hardest.

Keep practicing

Dependence misread

Independence, pairwise vs mutual, or correlation vs dependence.

See real exam options built on this mistake Drill statements like this

Go deeper· Explained in full in Sufficiency, completeness and the UMVUE machine· Asked in CSIR NET December 2025· From Estimation › Sufficiency, completeness, UMVUE, Cramér–Rao

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