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Foundational Proof

Proof that the Sample Mean is an Unbiased Estimator of the Population Mean

Students often misinterpret 'unbiased' to mean that a single sample mean Xˉ \bar{X} must equal the population mean μ \mu . Instead, it's a property of the *estimator* over repeated sampling, meaning E[Xˉ] E[\bar{X}] equals μ \mu in the long run, not for every specific instance.
Institutional Reference: Applied Statistics
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