Talk:Birthday problem: Difference between revisions

I’m not sure what “''Estimating the error in the estimate to help ensure the estimate is accurate to 4 decimal places''” means. My interpretation is that the <math>\sigma{_mean}</math>of the estimated frequency is <math><1/10000</math>.

The <math>\sigma{_mean}</math> of the distribution of each sample is calculated using the binomial distribution, so it’s is at most <math>1/2</math> (for <math>p=q=1/2</math>). We are very near that value.

In this case, if we use <math>\sigma{_mean}=\sigma /Sqrt(N)</math> then the number of samples has to be <math>N=25000000=10000^2/4</math>.

Most of the examples use <math>N=50000</math>, so they don’t have enough precision. On the other hand, <math>25000000</math> is to much, so I run my example in Racket with only <math>250000</math>, that gives a <math>\sigma</math> of only <math>1/1000</math>.

I think that the description of the task should ask for a clearer goal. For example: “''Do the final simulation with at least 25000000 samples to help ensure the estimate is accurate to 3 decimal places''.”