Part CCSIR NET December 2024the-maximum-estimates-the-other-endpoint

The maximum estimates the other endpoint

Let $X_{1}, X_{2}, \dots, X_{n}$ be a random sample of size n from $U (θ, θ + 1)$ distribution, where $θ \in R$ is the unknown parameter. If $T_{n} = min$ { $X_{1}, X_{2}, \dots, X_{n}$ }, n = 1, 2, …, then which of the following statements are true?

A. $T_{n}$ is an unbiased estimator of $θ$ .
B. $lim (n \to \infty) E_{θ} (T_{n}) = θ$ for all $θ \in R$ .✓
C. $T_{n}$ is a consistent estimator of $θ$ .✓
D.max{ $X_{1}, X_{2}, \dots, X_{n}$ } is a consistent estimator of $θ$ .

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.

See pricing

50 are analysed free — try those first.

Related counterexample: The MLE is unbiased

The maximum estimates the other endpoint

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