I thought the same, and tried it. The mean sample mean after 10 million runs is 500.47, which is very close to the true mean, 500.5. Bessel's correction is not correct here - it's effectively multiplying by n/(n-1), so your estimate would be 536. Bessel's correction is made for estimating true variance using a sample, not for estimating true mean.
Yes of course, the mean is the first moment and a Bessel correction would be inappropriate. Now I feel stupid. The mean calculated by sum(p_t x_i) or 1/n sum(x_i) is already the best linear unbiased estimate. Maybe we can't get better than twice the mean?
Comments
I thought the same, and tried it. The mean sample mean after 10 million runs is 500.47, which is very close to the true mean, 500.5. Bessel's correction is not correct here - it's effectively multiplying by n/(n-1), so your estimate would be 536. Bessel's correction is made for estimating true variance using a sample, not for estimating true mean.
Yes of course, the mean is the first moment and a Bessel correction would be inappropriate. Now I feel stupid. The mean calculated by sum(p_t x_i) or 1/n sum(x_i) is already the best linear unbiased estimate. Maybe we can't get better than twice the mean?