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Interview Question

Quantitative Analyst Interview

Consider an infinite set of pairwise independent random

  variables which are uniformly distributed between 0 and 1. What's the expected number that you need to add to get a number that exceeds 1.
Answer

Interview Answer

3 Answers

2

The answer is very pretty: it's e.

Interview Candidate on Nov 7, 2013
2

Could anyone explain why is e right answer ?

boibovski on Nov 16, 2014
4

Define f_m(n) to be 1 if m=0, x_1+..+x_k<=1 which is 1/k!. There are various ways to prove it: one is that there unit hypercube can be decomposed into k! copies of it (e.g. the square equals two triangles, the cube equals 6 tetrahedrons etc.)

Anonymous on Jan 5, 2015

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