A good estimator should satisfy certain criteria. Discuss these criteria with illustration.

In statistics, an estimator is a mathematical function that is used to estimate an unknown population parameter based on sample data. The accuracy of an estimator is crucial for making inferences about a population from sample data. Therefore, it is important to evaluate the properties of an estimator to determine its suitability for a given situation. In general, a good estimator should satisfy certain criteria, including unbiasedness, consistency, efficiency, and robustness.

1. Unbiasedness: An estimator is said to be unbiased if its expected value is equal to the true value of the population parameter being estimated. An unbiased estimator is preferred because it provides an average prediction that is equal to the true value of the parameter, which reduces the error in the estimation. Mathematically, an estimator is unbiased if E(θ_hat) = θ, where θ_hat is the estimator and θ is the true value of the population parameter.

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