When using the variance and covariance equations for both historical and probability based scenarios, when is the denominator simply n, and when is it n-1? i thought it would be based on the sample vs population issue, but I have seen schweser use n-1 for the denominator, and I do not think it mentioned that it was a sample ?

n is when you have a sample or pop # you dont use N with probs or historical data

Itâ€™s about whether or not you have to estimate the population mean. If you are given the population mean, use n. Otherwise use n-1

yeah sample mean must be based of n-1 cuz otherwise its baised. when used n-1 you get the variance as the UNBIASED ESTIMATOR.