Covering All Birthdays

Nice, this problem is isomorphic to the probability&#x2F;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”<p>There is a closed form solution to this problem’s expectation for arbitrary n and m, which I’ve linked below:<p><a href="https:&#x2F;&#x2F;math.stackexchange.com&#x2F;questions&#x2F;610250&#x2F;a-question-on-probability-hunter-and-rabbit" rel="nofollow">https:&#x2F;&#x2F;math.stackexchange.com&#x2F;questions&#x2F;610250&#x2F;a-question-o...</a>

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.<p><a href="https:&#x2F;&#x2F;lh3.googleusercontent.com&#x2F;proxy&#x2F;OZtu7ACWp4X283a4e5PgnmXyj4n6c9PsR_l3-Vd9ipFF4CoM9yiBZAwbFS9ZyNxxc_gZLihMZ-_n58Sw6W6NHGulybwBdHsu9S8" rel="nofollow">https:&#x2F;&#x2F;lh3.googleusercontent.com&#x2F;proxy&#x2F;OZtu7ACWp4X283a4e5Pg...</a>

If you&#x27;re going to write conditional probabilities with big parentheses don&#x27;t forget to make the \vert big as well. You can use \middle if you want to automatically match \left and \right.<p>Also conditional probabilities aren&#x27;t really the right tool when all you want is to set a parameter, but it works I guess.

Aren&#x27;t there 366 birthdays, not 365?<p>Are leap-day births unpersons?

I&#x27;m curious why the author thought it necessary to default to simulate a numerical distribution.<p>Perhaps maths is not taught or appreciated in CS much now.