Impact of Weighting Factor on Unbiasedness of Sample Means
Suppose a sample of random variables \(X_1, X_2, \dots, X_n\) have common mean \(\mu\) and variance \(\sigma^2\). A new estimator of \(\mu\) is defined by \(\hat{\mu} = \sum_{i=1}^n w_i X_i\), where \(w_i\) are weighting factors. Under what condition on the weights \(w_i\) is \(\hat{\mu}\) an unbiased estimator of \(\mu\)? Discuss the impact on unbiasedness if […]