When we have a sample of numbers, say
-69, 153, -54, 54, -198, -242, -63, 87, -45, -134, ...
we can calculate an estimation of the variance using the formula
now this formula applies to any sequence of numbers, regardless of its underlying distribution. But what if we know that these numbers are sampled from a normal distribution, can we provide a better estimate of the variance? And/or if we know the true mean?