Talk:Birthday problem

usage of people

Why assume that the people choosen are alive?   If dead, then "they" aren't people, but corpses.   The task clearly states a group of people.   However, even if dead, they still had a birthday. -- Gerard Schildberger (talk) 03:02, 4 November 2013 (UTC)

years in Algol

What does years signify in "%age of years with required common birthdays: 50.71%;" ? --Walterpachl (talk) 10:36, 4 November 2013 (UTC)

Meaning of precision

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 $\sigma _{\mathrm {mean} }$ of the estimated frequency is $<1/10000$.

The $\sigma _{\mathrm {mean} }$ of the distribution of each sample is calculated using the binomial distribution, so it’s is at most $1/2$ (for $p=q=1/2$). We are very near that value. In this case, if we use $\sigma _{\mathrm {mean} }=\sigma /Sqrt(N)$ then the number of samples has to be $N=25000000=10000^{2}/4$.

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

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.”