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From: Stephen Montgomery-Smith on 12 May 2010 18:02
atrovantes wrote:
>> atrovantes wrote:
>>> Hi,
>>> does anyone know any results about weighted sums of
>> Bernoullis?
>>>
>>> A simple example follows. Let X_n be i.i.d.
>> Bernoulli random variables. What's the distribution
>> of
>>> \sum_{k=1}^N X_k k ?
>>>
>>> Or if not the distribution maybe some other
>> results... Non-trivial of course (e.g. I can find the
>> mean myself).
>>>
>>> Thanx in advance.
>>
>>
>> I wrote a paper on this sort of thing:
>>
>> http://www.math.missouri.edu/~stephen/preprints/tail.h
>> tml
>
> Thanx for this. Your paper contains some stuff that I'm not familiar with, thus I need to take care of some prerequisites first.
>
> Are you aware of any other work on this subject?

I have some references to later works in these papers:

http://www.math.missouri.edu/~stephen/preprints/disttail.html
http://www.math.missouri.edu/~stephen/preprints/tailproc.html

Also, I should admit that this same result was also proved independently
by Montgomery and Odlyzko, and they predated me by about 2 years.

Finally, the results do involve "absolute constants", that is, numbers
that we know do not depend upon the parameters, but with little idea of
how large these constants actually are.

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