Variance Question
I've seen the empirical variance expressed two different ways and I don't understand when to use which.
i. Var = F*S/N
ii. Var = F*S*N
The later looks like the variance of a binomial which makes sense to me in situations where we want, say, the number of data points below a value, like F(1500). However, this is exactly the case in SOA #227, yet the solution uses the former (i). I don't understand why.
If we wanted the variance of F(1500) why wouldn't it be:
# pts below 1500/ N * # pts above 150 / N * N  because this would be variance of a binomial with F = p and S = (1p) * N.
When finding variance of grouped data, specifically, when the value we want is within a group, we use ii. Yet, in the simulation section we write the variance as in i.
Can someone explain simply what the difference is or why we use one or the other?
thanks.
