Does Sampling Variance Converge to Theoretical Variance in Simulations?

[jimmy1]

if a random variable X has variance sigma, does it mean that the average variance of X will be sigma, or will X always have variance sigma.
So if I did 10 simulations of the random variable X, is it plausiable that the variances differ widely, but the average of the variances converge to the theoretical variance, or do each of the variance have to be the same.

 

[mathman]

It looks like you are mixing up two different usages of the term variance. There is a theoretical variance which is fixed.

However the experimental variance can vary from experiment to experiment. The theoretical mean of the experimental variance is the theoretical variance.

 

[jimmy1]

Thanks, that cleared things up!

 

[ssd]

So if I did 10 simulations of the random variable X, is it plausiable that the variances differ widely, but the average of the variances converge to the theoretical variance, or do each of the variance have to be the same.

If you do not consider n-1 to be approximately equal to n, the avarage variance will not be equal to the theoretical variance nor do each of the sample variances will be same. Find 'expectation' of the sample (of size n) variance and check that it is not equal to theoretical variance.