tossing coins
From: Andersen (alibandali_at_hotmail.com)
Date: 08/21/04
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Date: Sat, 21 Aug 2004 18:04:52 +0200
I have a question regarding the distribution of a coin tossing
experiment. Somebody actually simulated the following experiment and
claims it is exponentially distributed. I would like to know if this is
common knowledge, or if it is false. So I describe the experiment:
I continously toss a coin with the outcome H or T. Assume also I have a
subset of the integers I = {1,...,N} for some large integer constant N.
I also have a set K = {N+1,..,2*N}.
Each time I toss my coin repeatedly with 1 seconds inter-arrival time I
do the following:
- If I get a H I randomly (with uniform distribution) remove one element
in K and add it to I.
- If I get a T, I do the reverse, ie. I remove an element randomly (with
uniform distribution} from I and add it to K.
I do this for sufficiently long time (infinitely). If we count the
number of seconds each integer was inside K before being removed, and
plot a frequency diagram over the "lifetime" of each integer in K, will
it be exponentially distributed? If so why?
Best regards,
Andersen
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