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Topic: Does uniform distribution of integers imply a uniform
distribution of their bits?

Replies: 2   Last Post: Feb 24, 2013 4:49 PM

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Herman Rubin

Posts: 399
Registered: 2/4/10
Re: Does uniform distribution of integers imply a uniform distribution of their bits?
Posted: Feb 24, 2013 4:49 PM
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On 2013-02-22, Ray Koopman <> wrote:
> On Feb 22, 10:59 am, Codeplug <> wrote:
>> Let's say I have a uniformly distributed set of 8-bit integers - [0, 255].
>> If those integers are then concatenated to form a string of bits, are those bits also uniformly distributed?

>> Thanks for the stat/math help :)
>> gg

> If the integers are uniform on [0, 2^n - 1], where n is a positive
> integer, then YES.

It is somewhat unclear what the question is. Uniformly distributed
does not mean independent and random. If they are also independent
and created by a uniform random process, this will also be the case
for the bits in the concatenated string.

This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University Phone: (765)494-6054 FAX: (765)494-0558

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