摘 要 常態分布之樣本平均數及樣本變異數具有下列統計性質:(1)二者均為充分統計量.(2)二者獨立.(3)樣本平均數為 MLE , UMVUE 及動差估計式.(4)樣本變異數為 MLE ,動差估計式,經適當修正可為 UMVUE .(5)二者之變異數為 Cramer-Rao 下界.(6) 二者均為漸近有效估計式.本文探討柏努力條件下,條件樣本平均數及條件樣本變異數是否 仍有上列性質 . Abstract The sample mean and sample variance of a Gaussian distribution have the following nice statistical properties:(1)both are sufficient,(2)they are independent, (3)sample mean is m.l.e., UMVUE, and method of momemt estimator,(4)sample variance is m.l.e.,method of moment estimator and UMVUE if multiplied by a constant, (5)both estimators have variances achieve the Cramer-Rao lower bound,(6)both estimators are asymptotically efficient.Based on sample obtianed from the conditional Gaussian distribution given Bernoulli distribution,we study conditional sample mean and conditional sample variance and check if they also have the above statistical properties.
