no
no
The proof that the sample variance is an unbiased estimator involves showing that, on average, the sample variance accurately estimates the true variance of the population from which the sample was drawn. This is achieved by demonstrating that the expected value of the sample variance equals the population variance, making it an unbiased estimator.
It is a biased estimator. S.R.S leads to a biased sample variance but i.i.d random sampling leads to a unbiased sample variance.
Yes, there is a mathematical proof that demonstrates the unbiasedness of the sample variance. This proof shows that the expected value of the sample variance is equal to the population variance, making it an unbiased estimator.
s2, using the Roman lower case letter.
No, it is biased.
The variance is: 1.6709957376e+13
You cannot prove it because it is not true.The expected value of the sample variance is the population variance but that is not the same as the two measures being the same.
No.
The mean, by itself, does not provide sufficient information to make any assessment of the sample variance.
It means you can take a measure of the variance of the sample and expect that result to be consistent for the entire population, and the sample is a valid representation for/of the population and does not influence that measure of the population.
The sample variance is 1.