If the data distribution is well-behaved (so that the central limit theorem applies or Hoeffding inequality) the size of the confidence interval is \(\delta\sim \frac{1}{\sqrt{N}}\) which means \(N\sim \frac{1}{\delta^2}\), now if you replace \(\delta\) by \(\delta/3\) this corresponds to replacing \(N\) by \( \frac{9}{\delta^2} = 9 N\).
exam 2019 pb 1
Hi,
I don't understand how do we find the new number of iid samples?
pb1_2019.JPG
Thank you so much!!
If the data distribution is well-behaved (so that the central limit theorem applies or Hoeffding inequality) the size of the confidence interval is \(\delta\sim \frac{1}{\sqrt{N}}\) which means \(N\sim \frac{1}{\delta^2}\), now if you replace \(\delta\) by \(\delta/3\) this corresponds to replacing \(N\) by \( \frac{9}{\delta^2} = 9 N\).
Add comment