Allstaters,
Please accept my apologies for a second posting. My earlier attempt
revealed some serious ambiguities in my formulation of the problem.
I wish to express my thanks to all those who tried to grapple with
my inadequate specification of the problem the first time.
Let me try again. Suppose that I run n iid Bernoulli processes
synchronously and in parallel. I define this as a meta-process.
This is run until meta-success is achieved, where meta-success
is defined as having achieved a success on EACH of the individual
processes. What is the number of trials (of the meta-process)
required to achieve meta-success?
Note 1. This is asking for the expectation of the maximum (no. of
trials) for n iid Bernoulli processes.
Note 2. Consider n=2 and p=0.5 as an example.
p(1)=1/4
p(2)=5/16
p(3)=13/64
p(4)=29/256
and so on.
Note 3. I note that I can get the probability for requiring exactly k
trials p(k) from the corresponding cdf by differencing thus:
p(1)=p**n
cdf(k)=(1-q**k)**n
p(k)=cdf(k)-cdf(k-1)
Thus I require the sum from k=1 to k=infinity of k*p(k) to
get the expectation that I require.
Allan
--
Dr. Allan White, Statistical Advisory Service, University of Birmingham
Tel. 0121-414 4750 or 44750 (internal), Email [log in to unmask]
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