2 ms·
You pointed out one error in your own answer, here's another. I haven't figured out the adjustments, but presumably they cancel. You've done ∫₀¹ ∫₀¹⁻ᶜ (2π r)³
by carstimon 8mo ago
You pointed out one error in your own answer, here's another. I haven't figured out the adjustments, but presumably they cancel.
You've done
∫₀¹ ∫₀¹⁻ᶜ (2π r)³ dr dc
However,
- the `dr` integral is assuming that the radii are uniformly likely in [0, r]
- the `dc` integral is assuming that the centers are uniformly likely in [0, c]
You need to wait these integrals by the conditional probability distributions.
- carstimon 8mo agoSorry, this was incorrect. In this integral we're just calculating the geometrical question, what is is the 5d volume of the collection of 3 points whose circumcenter is on {(x, 0) : x in [0, 1]}. So the "overall" probability of the problem has nothing to do with it.