Uniforms summing past 1

Draw U[0,1]U[0,1] values one at a time and add them until the running sum first exceeds 1. What is the expected number of draws? Give a decimal.

Show hints (2)+
  1. P(first n draws sum ≤ 1) is the volume of a simplex.
  2. That volume is 1/n!.

Answer

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2.718 (± 0.01)

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Asked at: Jane Street, Two Sigma

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