Testing random

[Thomas 'PointedEars' Lahn]

Ned Batchelder wrote:

> You aren't agreeing because you are arguing about different things.
> Thomas is talking about the relative probability of sequences of digits.

There is no such thing as “relative probability”, except perhaps in popular-
scientific material and bad translations.  You might mean relative 
_frequency_, but I was not talking about that specifically.

> Chris is talking about the probability of a single digit never appearing
> in the output.

I do not think that what I am talking about and what you think Chris is 
talking about are different things.

> Thomas: let's say I generate streams of N digits drawn randomly from 0-9.
> I then consider the probability of a zero *never appearing once* in my
> stream.  Let's call that P(N)
 
In probability theory, it is called the probability P(E) of the event E that 
in n trials the probability variable X never assumes the value 0, which can 
be defined as

  P(E), E = {e_i | n ∈ ℕ \ {0}, i = 1, …, n} \ {X ≠ 0}, Ω = {1, 2, …, 9} 

where the e_i are the singular events, or outcomes, of the probabilistic 
experiment, and Ω is the sample space of the e_i.

> Do you agree that as N increases, P(N) decreases?

I do not agree that P(E), as defined above, decreases as n increases.

See also: <http://rationalwiki.org/wiki/Gambler%27s_fallacy>

-- 
PointedEars

Twitter: @PointedEars2
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