Random Summation until One | Quant Interview Questions

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Question: You play a game where you sum independent identically distributed uniform random variables over the interval [0,1]. The first time the sum exceeds one, record the count of needed variables.

What is the expected number of variables?

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Special thanks to our Patreons:
Anik Roy
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Timecodes
00:00 - Question
00:18 - Understanding the Problem
00:58 - Solution
01:57 - Geometric Interpretation
03:21 - Hyperspaces and Final answer
07:05 - Coding Check
07:17 - Outro

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Book recommendations: atypicalquant.net/quant-books/

These should cover all the types of interview problems that one encounters at hedge funds such as Two Sigma (2sigma), Citadel, WorldQuant, BlackRock, Optiver, Jane Street, Akuna Capital, Hudson River Trading, etc.

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These animations are largely made using manim: github.com/3b1b/manim. Special thanks to 3Blue1Brown and the manim community!

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