4.1.3 Summary of numerical results

For the initial simulation run, we used \(20,000\) experiments and obtained the following estimate of the standard deviation and the population mean

\begin{align*} s & =0.625760\\ \bar {X} & =0.931717 \end{align*}

Now solve for \(n\) from

\[ 1.96\frac {s}{\sqrt {n}}=0.01\bar {X}\]

we found

\[ \fbox {$n=17328$}\]

Running the second stage simulation now to estimate the expected value of \(Y\) we obtain the following result that the estimate of the expected value of \(Y\) is

\[ \bar {X}=0.9311632 \]

and the \(95\%\) confidence interval was found to be

\[ \left \{ 0.92190\ \cdots \ 0.94043\right \} \]