Nice, this problem is isomorphic to the probability/graph theory problem “hunters and rabbits” from Matousek’s discrete math textbook, except with the slight modification that instead of “n hunters with perfect accuracy each randomly and simultaneously shoot one rabbit among a set of m rabbits”, it’s “n birthday havers each simultaneously have a birthday among m=365 days”
There is a closed form solution to this problem’s expectation for arbitrary n and m, which I’ve linked below:
The cover of Bayesian Data Analysis 3 shows that empirically, birthdays are not uniformly distributed. The fall has 10-20% more births than other months, and holidays are significantly underrepresented.
I think so. Parents can also make it happen at their convenience by asking doctors. We have technology to induce birth or control its timing over a few days
If you're going to write conditional probabilities with big parentheses don't forget to make the \vert big as well. You can use \middle if you want to automatically match \left and \right.
Also conditional probabilities aren't really the right tool when all you want is to set a parameter, but it works I guess.
Some cultures (not the US apparently) consider wishing an early birthday bad luck so I'd expect them never to celebrate on Feb 28. I know this is a thing in Central Europe, not sure how common it is. It was a big culture clash in a company I know when they moved HQ from Germany to the US because the Germans would get offended by Americans wishing them happy birthday when their birthdays were on the weekend or a bank holiday.
To spell it out: leap years happen less than every four years, so the average birth rate over four years is actually closer to 2,616 - quite outside the range of 6,574 - 12,301.
Because my maths is far weaker than my coding skills, I would have chosen simulation to give me a rough figure, rather than no answer; so the OPs simulation fascinated me when compared to the mathematical answer.
There is a closed form solution to this problem’s expectation for arbitrary n and m, which I’ve linked below:
https://math.stackexchange.com/questions/610250/a-question-o...