in which T is the total number of buses and t is the number of buses above observed bus number T0. In our case, T is between 2061 and 6184 with 50 per cent probability.
It is a correct claim, and saying that the total number of buses is double of the observed bus number is an oversimplification of that claim which we use only to point in the direction of the full Gott’s equation.
Ok. Thanks. So:
p(bus has number ≤ 1546 | city has 2992 buses) = 0.5
implies
p(city has < 2992 buses | bus has number 1546) = 0.5
?
If that is your reasoning, I do not see how you go from the former to the latter.
Is it a general fact that:
p(bus has number ≤ n | city has N buses) = p(city has < N buses | bus has number n)
or does it work only for 0.5?
May be we better take equation (2) from the original Gott’s work https://gwern.net/doc/existential-risk/1993-gott.pdf:
1 / 3 t < T < 3t with 50 per cent confidence,
in which T is the total number of buses and t is the number of buses above observed bus number T0. In our case, T is between 2061 and 6184 with 50 per cent probability.
It is a correct claim, and saying that the total number of buses is double of the observed bus number is an oversimplification of that claim which we use only to point in the direction of the full Gott’s equation.
Oh, it looks exactly like the kind of reference that everyone here seems to be aware of and I am not. ^^ I will be reading that. Thanks a lot.