the relationship of sample and true variance



Hi,everyone,
I have a question as following:
Suppose that X1, X2, ..., Xn is a random sample from the normal
distribution with mean and variance d*d the sample variance is S^2 =
[1 / (n - 1)] sum((Xi - M)^2),where M = (1 / n)sum( Xi)is the sample
mean. I wonder the relationship of d and S, any other simpler or rough
method to estimate their relationship besides the chi-square
distribution?
Thank you for your time.
Huijuan

.



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