Talk:Birthday problem: Difference between revisions

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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)

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

The $\sigma {_{m}ean}$ 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 $\sigma {_{m}ean}=\sigma /Sqrt(N)$ 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.”

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 What does years signify in "%age of years with required common birthdays: 50.71%;" ? --[[User:Walterpachl|Walterpachl]] ([[User talk:Walterpachl|talk]]) 10:36, 4 November 2013 (UTC)
+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''.”