Selection system - Gambling system

1. Jul 11, 2012

woundedtiger4

Hi all,

Currently I am trying to understand the concept of Selection System given in Billingsley's book "Probability and Measure". I have attached a pdf file with this post which consists on the scanned pages of this topic. I have understood it completely except one thing that how has the text calculated the values of "N_n". In the attached file there is an example 7.4 in which the values of N_1, N_2, N_3, and N_4 are given but I don't understand that how to calculate them or where have the come from though I do understand there role in the calculation of Y_n.

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2. Jul 11, 2012

micromass

The random variable $N_n$ indicates at what time the n'th bet will take place.

For example, if B1=0, B2=0, B3=1, B4=0, B5=1.

Then the first bet will occur in the 3th stage (because 3 is the first number n such that Bn=1). Thus N1=3.
The second bet will occur in the 5th stage (because 5 is the second number n such that Bn=1). Thus N2=5.

3. Jul 12, 2012

woundedtiger4

thank you sir.