Question

Which property of an estimator is satisfied if its expected value equals the population parameter?

• A. Consistency
• B. Efficiency
• C. Unbiasedness
• D. Sufficiency

Hint:

An estimator is \textbf{unbiased} if: \[ E(\hat{\theta}) = \theta \] This means the estimator gives the correct value of the parameter on average over many samples.

Answer 1

The Correct Option is C

Concept:
In statistical estimation, an estimator \( \hat{\theta} \) is said to be unbiased if its expected value equals the true population parameter \( \theta \). Mathematically, this is expressed as: \[ E(\hat{\theta}) = \theta \] This means that on average, the estimator correctly estimates the true parameter value.
Step 1: Understand the definition of an unbiased estimator.
If an estimator \( \hat{\theta} \) satisfies \[ E(\hat{\theta}) = \theta \] then the estimator does not systematically overestimate or underestimate the parameter.
Step 2: Identify the property.
The property that ensures the expected value of an estimator equals the population parameter is called Unbiasedness. \[ \therefore \text{The correct answer is Unbiasedness.
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