# Simple variance question

1. Feb 20, 2007

### 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.

2. Feb 21, 2007

### 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.

3. Feb 21, 2007

### jimmy1

Thanks, that cleared things up!

4. Feb 22, 2007

### ssd

If you do not consider n-1 to be approximately equal to n, the avarage variance will not be equal to the theoritical 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 theoritical variance.