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What this unbiased estimator question tests

This is a foundational statistics question that quant teams use to screen for understanding of estimation theory. It asks you to evaluate which of several candidate estimators for a Bernoulli parameter is biased — a core concept in both quantitative finance and machine learning inference.

To solve it, you compute the expectation of each estimator under the true data-generating process and check whether it equals the true parameter. An estimator is unbiased if its expectation matches the quantity you are trying to estimate; any deviation signals bias. The question tests whether you can apply this definition mechanistically and recognize which functional forms preserve or destroy the unbiased property.

• Definition and properties of unbiased estimators
• Expectations of transformed random variables
• Bernoulli distributions and independence