The Sample Mean is a Consistent Estimator of the Population Mean

In random sampling, the sample mean statistic is a consistent estimator of the population mean parameter. Not only is the sample mean an unbiased estimator for the population mean, but the variance of the sample mean approaches zero as the sample size n goes to infinity. The sampling distribution of the sample mean is centered on the population mean and its variance gets smaller and smaller as the sample size gets larger and larger.

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[samsonisaac]

Wow! Your explanations are very comprehensible, how i wish you can make other videos for the remaining properties of a good estimator

[samiraa]

what if the draws Xi are not independent and have a Cov(Xi, Xj)=ρ(σ)^2 ?