Print

---

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]