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Hello,

I was reading about the Central Limit Theorem today, in the study notes for Miller chapter 4 (p79 specifically), and I realized that I am unclear about the following:

(I) we indicate that the variance of each random variable is σ^2/n. As we have shown in the preceding ochapter, this is the variance of the sample mean. It makes sense. Each time we have a sample of n variables, defined by a sample mean and its variance. However we have also shown that the sample variance is an unbiased estimator of a population's variance ->

(II) In addition, I think I am slightly confused with our underlying population - are we interested in (a) the distribution of the sample means of our various samples, or (b) the distribution of each random variables (let's call them Xi). I know this is all related but I think it is linked to my confusion explained in point (I):

I hope I'm expressing this clearly enough! Thanks in advance for your feedback!

Florence

I was reading about the Central Limit Theorem today, in the study notes for Miller chapter 4 (p79 specifically), and I realized that I am unclear about the following:

(I) we indicate that the variance of each random variable is σ^2/n. As we have shown in the preceding ochapter, this is the variance of the sample mean. It makes sense. Each time we have a sample of n variables, defined by a sample mean and its variance. However we have also shown that the sample variance is an unbiased estimator of a population's variance ->

*why isn't the sample variance the variance of our sample, as opposed to the variance of the sample mean?*

(II) In addition, I think I am slightly confused with our underlying population - are we interested in (a) the distribution of the sample means of our various samples, or (b) the distribution of each random variables (let's call them Xi). I know this is all related but I think it is linked to my confusion explained in point (I):

*for me, σ^2/n is the variance of the sample mean, as opposed to the sample variance, which would be an unbiased estimator of the variance of a selection of n random variables Xi in an overall population of N.*I hope I'm expressing this clearly enough! Thanks in advance for your feedback!

Florence

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