To rephrase your objection to my more rigorous Poisson process treatment: "The assumption 'The Chelyabinsk meteor and the 2012 DA events are statistically similar events.' is questionable."
Your argument would clearly be reasonable if the size of theChelyabinsk meteor and the size of the 2012 DA asteroid were around the same. They weren't. The 2012 DA asteroid hit a much larger radius target but it was, itself, a much larger and therefore rarer size celestial object than was the Chelyabinsk meteor. It is not so easy to brush off my assumption as unreasonable. On Thu, Feb 28, 2013 at 6:58 PM, Daniel Rocha <[email protected]> wrote: > I don't think the coincidence that remote. You have to calculate the > probabilities as the asteroids were crossing spheres the size of of their > distance to earth. While the one that hit Russia hit Earth within its usual > radius, the more distant asteroid "hit Earth" with a radius as big as > Jupiter. That increases A LOT the probability of these kind of coincidences > since the total cross section is much higher for these kinds of events. > > > -- > Daniel Rocha - RJ > [email protected] > I've copied that more rigorous Poisson process treatment below: OK, since Paulson has pulled a hit and run (the "hit" occuring when he implied he had done a rigorous calculation of the odds and the "run" when I asked him to show his work), I'll show the work of an actual rigorous calculation: First of all, the correct treatment is as a Poisson process<http://www.math.ucla.edu/~hbe/resource/general/3c.2.05f/sec12-4-6.pdf> : P(k)=e^(-Λ)*Λ^k/k! Where P is the probability k = the number of times the rare event occurs Λ=λt λ= the rate per unit time t= the time interval over which the k rare events occur Assuming: The Chelyabinsk meteor and the 2012 DA events are statistically similar events. These events occur roughly every 100 years. Our unit of time is 1 hour. A human lifetime is 80 years. λ=1/(100year/1hour) 1/(100year/1hour) 1 / ([100 * year] / [1 * hour]) = 0.0000011415525 t=16 Λ=λt 0.0000011415525*16 = 0.00001826484 P(X=2)=e^(-Λ)*Λ^2/2! e^(-0.00001826484)*0.00001826484^2/2 ([e^-0.00001826484] * [0.00001826484^2]) / 2 = 1.6679914E-10 So, the odds of any particular 16 hour interval experiencing 2 of these rare events is about: 1/1.6679914E-10 1 / 1.6679914E-10 = 5.9952347E9 1 in 6 billion So in an 80 year lifespan the odds of experiencing such a coincidence is: 1-(1-1.6679914E-10)^(80years/16hours) 1 - ([1 - 1.6679914E-10]^[{80 * year} / {16 * hour}]) = 0.0000073057752 1/0.0000073057752 1 / 0.0000073057752 = 136878.01 about 1 in a hundred thousand.
