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# Bournelli, equation for variance? (with picture!)

1. So I was watching khan academy videos on Stats, and I noticed this:

why he does not calculate the variance of the sample he has first, and then approximate the variance of the normal distribution using the result?

Rest of the question is on picture in white text, any help much appreciated
Attached Images

3. What is M_1 (or mu_1) at the very start? And what is he trying to show, the normal distribution approximation for the sum of 1000 choices of 0 or 1 where the probability of choosing 1 is 0.642? In any case, that's a freaking tiny variance that can't be right for whatever
4. (Original post by Hopple)
What is M_1 (or mu_1) at the very start? And what is he trying to show, the normal distribution approximation for the sum of 1000 choices of 0 or 1 where the probability of choosing 1 is 0.642? In any case, that's a freaking tiny variance that can't be right for whatever
mu_1 is mean of sample number 1

He tries to show how many people have voted for a candidate (choice 1) and how many didn't (choice 0), by using this sample he then creates a normal distribution of all the sample means.
5. (Original post by Moa)
mu_1 is mean of sample number 1

He tries to show how many people have voted for a candidate (choice 1) and how many didn't (choice 0), by using this sample he then creates a normal distribution of all the sample means.
I'm still not sure what he's trying to show, that final super tiny variance makes no sense to me, sorry. Was there anything prior to this question he built upon?
6. (Original post by Hopple)
I'm still not sure what he's trying to show, that final super tiny variance makes no sense to me, sorry. Was there anything prior to this question he built upon?
Maybe the video can help you, if you have time to skim through it:

7. (Original post by Moa)
Maybe the video can help you, if you have time to skim through it:

Ah, I see. It builds on earlier videos (or so he says), but he's working out how the sample mean varies. He has worked out the variance of the first sample, but by a 'stock' formula (Bin(n,p) has variance np(1-p)), which gives the same answer as your more general formula. I'm assuming you're okay with the rest, just the calculation of the variance was different to what you expected?
8. (Original post by Hopple)
Ah, I see. It builds on earlier videos (or so he says), but he's working out how the sample mean varies. He has worked out the variance of the first sample, but by a 'stock' formula (Bin(n,p) has variance np(1-p)), which gives the same answer as your more general formula. I'm assuming you're okay with the rest, just the calculation of the variance was different to what you expected?
Yes that is it, its all clear now, I can see that the results of "mine" and his formulas are very close.

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