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Putnam 2020 B3

Source: 81st William Lowell Putnam Competition

February 22, 2021
Putnamprobabilityexpected valuefunctionPutnam 2020

Problem Statement

Let x0=1x_0=1, and let δ\delta be some constant satisfying 0<δ<10<\delta<1. Iteratively, for n=0,1,2,…n=0,1,2,\dots, a point xn+1x_{n+1} is chosen uniformly form the interval [0,xn][0,x_n]. Let ZZ be the smallest value of nn for which xn<δx_n<\delta. Find the expected value of ZZ, as a function of δ\delta.
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