Where the arrivals land

Trades hit a venue as a Poisson process. Given that exactly 33 trades arrived during a one-hour session, what is the probability that exactly 22 of them fell in the first 2020 minutes of the hour? (to 3 decimals)

Show hints (2)+
  1. Given the count, arrival times are independent Uniform draws over the interval.
  2. Each of the 3 lands in the first third with prob 1/3; count "2 of 3" with a binomial.

Answer

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0.2222 (± 0.005)

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Asked at: Jane Street, Two Sigma

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