Population: The entire group of individuals or items about which information is desired.
Sample: A subset of the population selected for study.
Parameter: A numerical measure describing a characteristic of the population (e.g., population mean μ).
Statistic: A numerical measure describing a characteristic of a sample (e.g., sample mean X̄).
Estimator: A rule or formula used to estimate an unknown population parameter from sample data.
Estimate: The actual numerical value obtained from the estimator applied to a given sample.
Point Estimation involves using a single value from the sample to estimate an unknown population parameter. For example, the sample mean X̄ is used as a point estimate of the population mean μ.
An estimator θ̂ is said to be unbiased for θ if its expected value equals the true parameter value.
Unbiasedness
E(θ̂) = θ
Example: Sample mean X̄ is an unbiased estimator of population mean μ,
because E(X̄) = μ.
Sample variance S² = Σ(Xi - X̄)² / (n-1) is unbiased for σ².
Note: If we divide by n instead of (n-1), the estimator becomes biased.