Raul: I understand what you are trying to do, but I believe it has the same problem as we have had before:
- A statistic (e.g. the sample mean) is a random variable: it is different from its value on an actual sample. - The expectation of a statistic is different from its value on an actual sample. The distribution of a statistic depends on the population distribution. Its expected value depends on the population distribution. Since we are trying to use a statistic to tell us something about the population, we seem to be in a chicken and egg situation: the population has an unknown distribution, and the statistic depends on this. The idea of the case we are discussing is to estimate the population variance without knowing anything about the population distribution. This is point estimation, and the proof I gave shows that this can be done, namely that E(S^2)=\sigma^2. To see how accurate our estimate is, we would need to know something about the population distribution and how this affects the distribution of the statistic, and we cannot do it in general. If the population is normal, then some multiple of our estimate has the chi-squared distribution, so we can do things like construct confidence intervals for the estimate. However, it is not the case that E(\sum (X_i-\bar X)^2)=\sum (x_i-\bar x)^2 any more than it is the case that the expected value of the sample mean is the same as its value on an actual sample. If you are trying to calculate an expected value by averaging it over samples taken from the population, you will get an estimate, but what does it mean? This is precisely what estimation is about. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
