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What is an unbiased estimator? Proof sample mean is unbiased and why we divide by n-1 for sample var

In this video I discuss the basic idea behind unbiased estimators and provide the proof that the sample mean is an unbiased estimator. Also, I show a proof for a sample standard variance estimator that uses n in the denominator, and show that it is a biased estimator, therefore we use n-1 in the denominator to obtain an unbiased estimator for the population variance.