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Part BCSIR NET June 2023

Sufficiency, completeness, UMVUE, Cramér–Rao

Let X be a Poisson random variable with mean λ\lambda. Which of the following parametric functions is not estimable?

  1. A.λ\lambda⁻1^{1}✓ Correct
  2. B.λ\lambda
  3. C.λ2\lambda^{2}
  4. D.e−λe^{-\lambda}

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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Related counterexample: A sufficient statistic is complete

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The chapter behind this: Sufficiency, completeness and the UMVUE machine — free to read

From Estimation › Sufficiency, completeness, UMVUE, Cramér–Rao

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